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### About Basic Data Descriptors, Statistical Distributions, and Application to Business Decisions Course

Business Statistics are growing more essential. To correctly evaluate data, you must grasp Business Statistics. Lack of understanding might lead to wrong decisions that hurt a company. This course teaches Business Statistics. Descriptive statistics summarises data using a few numbers. Different descriptive measures and Excel tools to calculate them are introduced. Using business examples, probability or uncertainty, samples, and population data are introduced. This leads to statistical distributions and Excel formulas used to simulate or approximate business processes. Throughout the course, you use descriptive data metrics and statistical distributions using Excel examples.

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## Basic Data Descriptors, Statistical Distributions, and Application to Business Decisions Quiz Answers

#### Quiz 1: Descriptive Statistics

Q1. You can calculate the mean of the order dollar amounts using any of the formulas below EXCEPT:

• =AVERAGE(B2:B6)
• =(B2+B3+B4+B5+B6)/5
• =MEAN(B2:B6)
• =SUM(B2:B6)/COUNT(B2:B6)

Q2. The data shown above has one “extreme” observation relative to the others. In this case, which of the following is true? Select all that apply.

• The Median of this data is a larger dollar amount than the Mean of this data.
• The Mean of this data is a larger dollar amount than the Median of this data.
• The Median more accurately reflects the typical data when the extreme observations are removed.
• The Mean more accurately reflects the typical data when the extreme observations are removed.

#### Quiz 2: Descriptive Statistics Continued

Q1. In the histogram above, which of the following is true?

• The data is skewed to the right, and Mean > Median.
• The data is skewed to the right, and Mean < Median.
• The data is skewed to the left, and Mean > Median.
• The data is skewed to the left, and Mean < Median.

Q2. Given the range and percentages above, calculate the Inter Quartile Range (IQR).

`Enter answer here`

#### Quiz 4: Introduction to the Box Plot and the Standard Deviation

Q1. In the Box Plot above, what is the Median?

`Enter answer here`

Q2. Which of the stocks above has the smallest Standard Deviation?

(No calculations are necessary, just take a look at the data in the table and use what you know about the Standard Deviation!)

• Stock A
• Stock B
• Stock C
• All three stocks have the same Standard Deviation

#### Quiz 5: The Standard Deviation “Rule of Thumb”

Q1. At Company ABC, the Variance of the dollar amount collected per sale is 85. Based on this information, the Standard Deviation of the dollar amount collected per sale is:

(Note that variance is the square of standard deviation)

• Less than \$85.
• Greater than \$85.
• Equal to \$85.
• Not related to the Variance.

Q2. At Company ABC, you would expect the number of sales within ± 1 Standard Deviation from the Mean to be:

• Approximately 35% of the total number of sales.
• Approximately 49% of the total number of sales.
• Approximately 68% of the total number of sales.
• Approximately 95% of the total number of sales.

#### Quiz 6: Testing the “Rule of Thumb”

Q1. The formula used to calculate the Interquartile Range for cells C2 through C12 is incorrect. It contains the following errors (select all that apply):

• The cell ranges in the formula refer to the wrong column.
• The cell ranges in the formula refer to the wrong rows.
• The 1st quartile is incorrectly added to the 3rd quartile.
• The Mean is incorrectly left out of the formula.

Q2. How could you edit cell F6 to return Mean + 2 Standard Deviations?

• = 2*(F1 + F4)
• =F1 + F4
• = F1 + 2*F4
• = 2*F1 + F4

#### Quiz 7: Chebyshev’s Theorem

Q1. Select all answers that hold true for Chebyshev’s Theorem.

• It holds for any distribution shape.
• It is another name for the 68%/95% “rule of thumb.”
• It states that at least 75% of all values are within ±2 standard deviations from the mean.
• It is always true.

Q2. True or False: at least 75% of all values in the distribution above are within ±2 standard deviations from the mean.

• TRUE
• FALSE

#### Quiz 8: Basic Data Descriptors and Data Distributions

Q1. Download the file “OrderList.xlsx.” This file contains basic customer order information, including an order number, the region where the order was placed, the age of the customer, and the total dollar amount of the order. Use the data in this file for the remainder of the assignment.

Note: Please use a “.” instead of a “,” to indicate a decimal point.

The total number of orders in the “OrderList.xlsx” file is:

`Enter answer here`

Q2. The median of “Total Sale \$” is larger than the mean. By how much? Round to 2 decimal places.

`Enter answer here`

Q3. What is the standard deviation of Total Sale? Round to 2 decimal places.

`Enter answer here`

Q4. What percentage of orders fell within the interquartile range of Total Sale?

`Enter answer here`

Q5. What is the approximate shape of the distribution of total sales? (Hint: Create a histogram to see, or use what you know about the mean/median relationship and the rule of thumb.)

• The distribution is uniform.
• The distribution is symmetric.
• The distribution is skewed right.
• The distribution is skewed left.

Q6. Given the limited information you have, your boss wants you to group customers in a meaningful way. You decide to take a look at how the order region impacts things. Calculate the average total sales from the North region only. What is the difference between the North region average total sales and the average total sales across all regions (including the North)? Round to 2 decimal places.

[Note: To calculate the average total sales from the North region only you could either “sort” the data and calculate the average or “filter” the data, copy and paste as values and then calculate the average. Please refer to Course 1 of this specialization for details on sorting and filtering data]

`Enter answer here`

Q7. What is the absolute value of difference between the North region median total sales and all orders median total sales (across all regions including the North)?

[Note: To calculate the median total sales from the North region only you could either “sort” the data and calculate the median or “filter” the data, copy and paste as values and then calculate the median. Please refer to Course 1 of this specialization for details on sorting and filtering data]

`Enter answer here`

Q8. Next, take a look at customer age. Create 3 age groups: 21-30, 31-40, 41-50. What is the average total sales for the age group with the highest average? Round to 2 decimal places.

`Enter answer here`

Q9. What is the median total sales of the age group with the highest average Total Sales? Round to 2 decimal places.

`Enter answer here`

Q10. Given the mean and median of the group with the highest average sales, what can you say about the distribution of total sales within that group?

• The distribution is uniform.
• The distribution is normal.
• The distribution is skewed right.
• The distribution is skewed left.

Q11. Based on this data, what would you recommend to your boss?

• We should separate customers by region and target the North region as our main customer segment. That segment has historically brought in higher average total sales.
• We should separate customers by age group and target 21-30 as our main customer segment. That segment has historically brought in higher average total sales.
• We should separate customers by age group and target 31-40 as our main customer segment. That segment has historically brought in higher average total sales.
• We should separate customers by age group and target 41-50 as our main customer segment. That segment has historically brought in higher average total sales.

#### Quiz 1: Covariance

Q1. In the chart above, the covariance of Series1 and Series 2 is

• Positive
• Negative
• Both positive and negative
• Zero

Q2. In the chart above, the covariance of Series1 and Series 2 is

• Positive
• Negative
• Both positive and negative
• Zero

#### Quiz 2: Correlation

Q1. Variables A and B have a covariance of 45, and variables
C and D have a covariance of 627. How
does the A and B relationship compare to the C and D relationship?

• A and B are more positively related than C and D.
• C and D are more negatively related than A and B.
• A and B are more negatively related than C and D.
• Not enough information is given to compare the two relationships.

Q2. Correlation Matrix:

Provided above is the correlation matrix that contains pairwise correlations across four variables. Based on this correlation matrix, which pair of variables has the largest positive correlation?

• A,B
• A,C
• A,D
• B,C
• B,D
• C,D

#### Quiz 3: Causation

Q1. To establish causation (select all that apply):

• The two
variables must be correlated.
• The causing variable must occur before the caused variable.
• External variables must be ruled out.
• The two variables must have a strong positive correlation.

Q2. There is a positive correlation between ice cream consumption and shark attacks. However, ice cream consumption does not cause shark attacks, because:

• Ice cream could not be eaten before a shark attack.
• External variables, like warm weather, could impact both ice cream consumption and shark attacks.
• There is no correlation between ice cream consumption and shark attacks.
• Sharks prefer frozen yogurt.

#### Quiz 4: Probability

Q1. A bag contains 5 red balls and 15 white balls. Without looking into the bag, what is the
probability that you will choose a red ball? Give your answer as a probability with 2 decimal places.

`Enter answer here`

Q2. A fair coin is tossed and comes up heads 3 times in a row. On the next coin toss, the probability of a heads outcome is:

• 0.25
• 0.33
• 0.50
• 0.75

#### Quiz 5: Statistical Distributions

Q1. Which of the following are examples of continuous data?

• The amount of water in a bucket.
• The number of bees in a beehive.
• The distance traveled on a road trip.
• The grains of sand in the universe.

Q2. True or false: Continuous distributions can be used to model discrete data.

• TRUE
• FALSE

#### Quiz 6: Descriptive Measures of Association, Probability, and Data Distributions

Q1. Download the file “Datasets.xlsx” Use the data in this file for the remainder of the assignment.

How many rows of data are included in the datasets given?

`Enter answer here`

Q2. What is the covariance of Datasets A and B? Round to 2 decimal places.

`Enter answer here`

Q3. Which dataset pair has the highest covariance?

• A & B
• B & C
• A & C
• Cannot be determined with the information given.

Q4. Which dataset pair has the strongest relationship?

• A & B
• B & C
• A & C
• Cannot be determined with the information given.

Q5. Given that dataset A outcomes always occur before dataset B outcomes (and no other information), can you conclude that A causes B?

• Yes, because all requirements for causation are met.
• Yes, because covariance and correlation are both positive.
• No, the variables are not correlated.
• No, there is no control for external variables.

Q6. Create a histogram of Dataset A. Based on the shape of the distribution of outcomes, which of the following is most likely true?

• Higher values are much more likely to occur than lower values.
• Negative values are much more likely to occur than positive values.
• All values in the range have a relatively equivalent chance of occurring, with a slightly lower probability on the high end.
• No information can be used from this dataset.

Q7. Create a histogram of Dataset B. Based on the shape of the distribution of outcomes, select the range below that appears to have the highest probability of occurrence.

• -729 to -350
• -250 to 200
• 400 to 800
• 1100 to 1500

Q8. Consider 4 sets of data:

set W: set of all real numbers over the range 1 to 100.

set X: set of all integers over the range 1 to 100.

set Y: set of all real numbers over the range 1 to 3.

set Z: set of all whole numbers over the range 1 to 10,000.

Which set has the LEAST numbers?

• set W
• set X
• set Y
• set Z
• Cannot be determined from the information given.

Q9. Assume that datasets Y and Z have a Covariance of -500. Which of the following do you know to be true? Select all that apply.

• Datasets Y and Z have a strong relationship.
• Datasets Y and Z have a negative relationship.
• The results may be affected by the units of measurement.
• Datasets Y and Z have a causal relationship.

Q10. Select all the examples of Discrete data below:

• Bees in a behive
• Honey in a beehive
• Fish in the sea
• Voltage level of a battery
• Time you wake up in the morning
• Languages spoken
• Voters for a particular candidate in an election
• Cooking oil used in recipe
• Animals on a farm

#### Quiz 1: PDF and PMF

Q1. A probability mass function (pmf) describes a variable, X, that has 3 possible outcomes. Outcome 1 has a probability of 25% and outcome 2 has a probability of 25%. What is the probability of outcome 3?

`Enter answer here`

Q2. A probability density function (pdf) describes a variable, Y, that has an infinite number of outcomes between points A and B. What is the probability of an outcome that is exactly halfway between points A and B?

`Enter answer here`

#### Quiz 2: The Normal Distribution

Q1. The area under the curve of a Normal Distribution is
equal to:

`Enter answer here`

Q2. Any particular Normal Distribution can be uniquely defined by two parameters. The first parameter is also the of the distribution and the second parameter is also the of the distribution.

• Variance, Median
• Standard deviation, Mean
• Mean, Mode
• Mean, Standard deviation

#### Quiz 3: The NORM.DIST Function

Q1. X ~ Normal(1.7, 8)

The standard deviation of the random variable X is:

`Enter answer here`

Q2. The Excel function

=1 – NORM.DIST(25, 50, 10, TRUE)

describes the probability of an outcome that is:

• less than 50 in a distribution centered at 10
• greater than 50 in a distribution centered at 25
• less than 25 in a distribution centered at 50
• greater than 25 in a distribution centered at 50

#### Quiz 4: The NORM.DIST Function Continued

Q1. The probability of the shaded region of the above Normal Distribution (mean = 5 and std deviation = 2) is:

• = NORM.DIST(7.5, 5, 2, TRUE) – Norm.DIST(5, 5, 2, TRUE)
• = 1 – Norm.DIST(7.5, 5, 2, TRUE)
• = NORM.DIST(7.5, 5, 2, TRUE)
• = NORM.DIST(5, 5, 2, TRUE) – Norm.DIST(7.5, 5, 2, TRUE)

Q2. In a Normal Distribution with a mean of 100, Prob(X > 120) is

• greater than Prob(X ≥ 120)
• less than Prob(X ≥ 120)
• equal to Prob(X ≥ 120)
• Not enough information to determine any of the three relationships listed out.

#### Quiz 5: The NORM.INV Function

Q1. The Normal Distribution above has mean = 5 and standard deviation = 2. If the probability of the shaded region is 0.20, how could you determine z such that
Prob(outcome > z) = 0.20?

• =NORM.INV(0.20, 5, 2)
• =NORM.INV(0.20, 2, 5)
• =NORM.INV(0.80, 5, 2)
• =NORM.INV(0.80, 2, 5)

Q2. =NORM.INV(0.5, 10, 2.35) will return the value:

`Enter answer here`

#### Quiz 6: The Normal Distribution

Q1. A new airline company has a commuter airplane that can hold up to 64 passengers. The plane flies a single route and charges passengers \$300 for a one-way fare. All fares are 100% refundable if the passenger does not show up for the flight. The fixed cost (the cost that does not change with the number of passengers, such as crew salaries, airport fees, etc) for every flight is \$1,000. The variable cost (the additional cost per passenger) for every flight is \$150 per passenger.

Create a spreadsheet that calculates the total profit per flight based on the number of passengers on the plane. What is the total profit if they fly with 56 passengers?

HINT:

1. Create a column of “Total number of passengers”, put in values 1 through 64
2. The next column would be “Variable Cost”. Put in values in this column, for example if you fly with 1 passenger the variable cost is \$150, if with 2 passengers then it is 2\$150, with 15 passengers it is 15\$150 and so on.
3. The third column would be “Total Cost” which is the “Variable Cost” plus “Fixed Cost”, i.e. the number in the Variable Cost column plus \$1000
4. The fourth column would be “Revenue” column which is “Total number of passengers”\$300. That is if the plane only carries 1 passenger then the revenue is 1\$300, if it carries 43 passengers then revenue is 43*\$300 and so on.
5. The fifth column would be “Profit” column which simply is “Revenue” column minus the “Total Cost” column.
6. Once you have created this “Profit” column then read off the value of profit when the plane flies with 56 passengers. That is your answer.
`Enter answer here`

Q2. Because they have a full refund policy, it is common for customers not to show up. Airline company management is wondering if it would make financial sense to overbook the flight and risk having not enough seats for all passengers that show up. In that case, the airline would find volunteers to give up their seats in exchange for a free ticket to the same destination on the next available flight. This would cost \$100 for each overbooked passenger.

Update your spreadsheet to account for overbooked passengers. What is the total profit if they fly with 64 passengers after having sold 72 tickets, assuming all 72 passengers show up?

`Enter answer here`

Q3. If 80 tickets are sold, the number of passengers expected to show up can be approximated by a normal distribution with a mean of 68 and standard deviation of 5. Therefore, if the airline sells 80 tickets for the flight, what is the probability that the number of passengers who show up will result in an overbooked flight? Enter your answer as a decimal probability (not a percent) rounded to 4 decimal places.

`Enter answer here`

Q4. Fill in the blank:

Using the same distribution as the previous question, there is a 0.10 probability that more than _ passengers show up. Please round your answer to the lowest integer.

`Enter answer here`

Q5. Continuing with the same distribution, what is the probability that less than or equal to 60 passengers show up? Enter your answer as a decimal probability (not a percent) rounded to 4 decimal places.

`Enter answer here`

Q6. XYZ Company produces copper pipes to be supplied to a local utility company. The requirement of the utility company is that the pipes need to be 200 cm of length. Longer pipes are acceptable to the utility company but any pipe less than 200 cm is summarily rejected and has to be scrapped. The XYZ Company loses all its production cost on pipes that are rejected.

The production process is such that it has some variability in the lengths of pipes produced, and this variability can be well approximated by a Normal distribution. The company can adopt one of the following three production processes:

Process A: Produces pipes with an average length of 200 cm and a standard deviation of 0.5 cm

Process B: Produces pipes with an average length of 201 cm and a standard deviation of 1 cm

Process C: Produces pipes with an average length of 202 cm and a standard deviation of 1.5 cm

If the company adopts the third Process (Process “C”), what is the probability it will have its pipe rejected by the utility company? Enter your answer as a decimal probability (not a percent) rounded to 4 decimal places.

`Enter answer here`

Q7. The utility company temporarily changes its requirements and
has a new requirement that it will accept any pipe of length from 199 cm till
202 cm. That is, pipes ranging in length from 199 cm to 202 cm will be
accepted, others will be rejected.

With this changed requirement which Production process (out
of the three) will result in the least % of rejections?

• Process A
• Process B
• Process C

Q8. XYZ Company earns a revenue of \$200 for every pipe that gets accepted and loses all money for any pipe
that is rejected. The cost of producing the pipes is \$140 per pipe if
production process “A” is used, \$160 per pipe if production process “B” is
used, and \$177 per pipe if production process “C” is used.

Given this information, which production process would you
recommend to maximize profits (revenue minus cost) if the requirement of the
utility company is that pipes need to be of 200 cm (or more) and any pipe less
than 200 cm is rejected?

• Process A
• Process B
• Process C

#### Quiz 1: Applying the Normal Distribution, Standard Distribution

Q1. An ice cream truck driver sells both chocolate and vanilla ice cream cones. In a specific neighborhood, the demand for chocolate and vanilla ice cream can be approximated by the following normal distributions:

Chocolate_Demand ~ Normal(79 cones, 25 cones)

Vanilla_Demand ~ Normal(65 cones, 37 cones)

If the driver wants to be at least 95% sure that she will not run out of vanilla cones, she could determine the number of vanilla cones to prepare with which of the following formulas?

• =NORM.INV(95, 65, 37)
• =NORM.INV(0.95, 65, 37)
• =NORM.INV(95, 79, 25)
• =NORM.INV(0.95, 79, 25)

Q2. Suppose Y ~ Normal(55, 5). How could you transform this variable into another random variable Z that follows the Standard Normal Distribution?

• Z = (Y + 55)*5
• Z = (Y – 5)/55
• Z = (Y – 55)/5
• Z = (Y + 5)*55

#### Quiz 2: Population and Sample data

Q1. You run a business and want to determine the average amount your current Canadian customers purchase per year. What is the relevant population?

• All potential customers living in Canada.
• All current customers living in Canada.
• All consumers living in Canada.
• All customers that have made a purchase in the past.

Q2. If you wanted to collect a representative sample of the attendees of a sporting event, you could

• Randomly select from people in the beer line.
• Randomly select from people wearing team colors.
• Randomly select from people with parking passes.
• Randomly select from people on the ticket holder list.

#### Quiz 3: Central Limit Theorem

Q1. If you are given a mean and standard deviation denoted as x̅ and s, respectively, you know that you are dealing with a:

• Sample of a population
• Population
• Random sample
• Normal Distribution

Q2. You know that the distribution of a specific population is a Uniform Distribution (i.e., not a Normal Distribution). The Central Limit Theorem states that the sample mean will have a(n):

• Uniform distribution
• Normal distribution
• Discrete Distribution
• Continuous Distribution

#### Quiz 4: The Binomial Distribution

Q1. Which of the following could be modeled as a Bernoulli
Process? Select all that apply.

• The probability of getting heads in a coin toss.
• The probability that your cat is awake.
• The probability of rolling a 2 on a fair, 6-sided die.
• The probability of rolling a 4, 5, or 6 on a fair, 6-sided die.

Q2. You flip a coin 5 times in a row. The equation

=1 – BINOM.DIST(3, 5, 0.5, TRUE)

gives the probability that:

• You get heads 3 times.
• You get heads 4 or 5 times.
• You get heads less than or equal to 3 times.
• You get 5 heads in a row.

#### Quiz 5: Business Application of the Binomial Distribution

Q1. At a manufacturing plant, the rate of a specific product being defective is 2%. If the company randomly audits 400 units of this product, what is the probability that the auditors will catch at least 20 defective units?

P(DefectiveUnits ≥ 20) =

• 1 – BINOM.DIST(19, 400, 0.02, TRUE)
• BINOM.DIST(20, 400, 0.02 , TRUE)
• BINOM.DIST(20, 400, 0.02, FALSE)
• 1 – BINOM.DIST(20, 200, 0.02, TRUE)

Q2. In the question above, what is the mean of the Binomial Distribution?

• 4 units
• 8 units
• 20 units
• 200 units

#### Quiz 6: Poisson Distribution

Q1. Which of the following examples have an underlying variable that can be well approximated by the Poisson Distribution?

• The number of customers that walk into a bakery on a particular Thursday.
• The odds of rolling a 3 on a fair, 6-sided die.
• The number of patients making doctor appointments in a specific week.
• The number of customers that show up at a fast food restaurant every 10 minutes.

Q2. A civil engineer uses a Poisson distribution to approximate the number of cars that arrive at a single-lane drawbridge each day during the week. He estimates from past data that on average, 230 cars arrive each day. What is the probability that fewer than 200 cars arrive at the drawbridge on a given day?

• = POISSON.DIST(200,230,TRUE)
• = POISSON.DIST(200,230,FALSE)
• = POISSON.DIST(199,230,TRUE)
• = 1- POISSON.DIST(199,230,TRUE)

#### Quiz 7: Working with Distributions (Normal, Binomial, Poisson), Population and Sample Data

Q1. You make widgets. You want to sell your widgets at the nearby widget store, since this would potentially increase your sales. However, you would have to pay a transportation cost every day to send you widgets over to the store. You decide to run some calculations to see if you would be at risk of losing money due to the transportation costs.

You know that 5 other widget companies sell widgets at that store, so you would be the 6th. Assuming a customer is equally likely to select any of the widgets, what is the probability they will select and purchase your widget? Write your answer as a probability (not a percent) rounded to 4 decimals.

`Enter answer here`

Q2. The widget store owner tells you that 200 customers arrive and purchase a widget from the store each day. Assuming you must sell 30 of your widgets to cover the transportation costs, and given the probability you calculated in question 1, use a binomial distribution to estimate the probability of at least covering the transportation costs (that is, the probability of selling at least 30 widgets). Write your answer as a probability (not a percent) rounded to 4 decimals.

`Enter answer here`

Q3. How many minimum number of people would have to visit the store to give you at least a 0.95 probability of covering the transportation costs?

HINT: Use the BINOM.DIST function trying out various values for “n”, the number of trials.

`Enter answer here`

Q4. The widget store manager points out that not all widget brands get equal purchase rates. A brand on premium shelf space has a 0.28 probability of being selected by each customer. He is willing to give you premium shelf space at the front of the store for a small fee. The additional fee, plus the original transportation costs, would raise the minimum number of widgets you would have to sell to 40 (to cover transportation costs and additional fee).

Assuming 200 customers come into the store, use a binomial distribution to estimate the probability of at least covering the transportation costs and additional fee. Write your answer as a probability (not a percent) rounded to 4 decimals.

`Enter answer here`

Q5. The widget store manager reminds you that while the average number of people that show up each day is 200, the actual number varies. He tells you that the customers that show up each day can be modeled with a Poisson distribution where lambda = 200.

What is the probability that at least 200 customers arrive (that is, either 200 or more than 200 customers arrive)? Write your answer as a probability (not a percent) rounded to 4 decimals.

`Enter answer here`

Q6. How many minimum number of people would have to visit the store to give you at least a 0.95 probability of covering the transportation costs and the additional fee? Use as 0.28 the probability of a widget being selected by a person.

HINT: You need to sell at least 40 widgets to cover transportation cost and the additional fee. So the number of “successes” need to be greater than equal to 40. The probability of “success” in each trial is 0.28. Now use the BINOM.DIST function trying out various values for “n”, the number of trials.

`Enter answer here`

Q7. You are curious about the accuracy of the estimates that the widget store owner gave you. If you wanted to take a random sample of daily customer arrivals, from which of the following is the population you should sample?

• The number of arrivals each day for this widget store and the competing widget store down the street.
• The number of arrivals each day for all days this specific widget store has been open.
• The number of arrivals each day for this specific widget over the past month.
• A random, representative sample of the number of arrivals each day to this specific widget store.

Q8. The store owner gives you data on customer arrivals over the last 3 years. You randomly select a sample of daily customer arrivals, and then take the mean of that sample. If you were to repeat this process multiple times, you would expect the distribution of the sample means to be:

• A Normal Distribution
• A Binomial Distribution
• A Poisson Distribution
• The same distribution as the population of interest

Q9. Assuming the widget store owner’s original estimates (given in Question 5) are accurate, what would you expect the mean of the distribution above to be?

`Enter answer here`

#### Syllabus Content:

Students will need access to Microsoft Excel in order to complete course assignments.

WEEK 1
Module 1: Characteristics of Data
In this lesson, you’ll learn how to recognize, compute, and analyze a variety of descriptive and summary measurements of data. These numerical metrics are used to describe and summarise data. The proper Excel functions to perform these computations are presented and shown as examples.

Measures of central tendency, including the mean, median, and mode, and their meanings and calculations, are discussed, as well as the many categories of descriptive data.
Box plots Range, interquartile range, standard deviation, variance, and the rule of thumb and Chebyshev’s theorem for interpreting standard deviation
___________________________

WEEK 2
Submodule 2: Association, Probability, and Statistical Distribution Measures
In this lesson, you will learn how to use Excel’s built-in covariance and correlation functions. In this lesson, you will learn the difference between correlation and causality. Following this, the module begins its introduction of statistical distributions and the concepts of probability and random variables.

Measures of association (such as covariance and correlation) are discussed, as are issues of causality vs. correlation.
The differences between continuous and discrete data; probability and random variables
Distributed data: a primer

WEEK 3
Unit 3: The Normal Distribution
This lesson covers the basics of the Normal distribution and how to use an Excel function to determine probabilities and outcomes based on the Normal distribution.

Included are discussions on: • The area under the curve as a measure of probability and the probability density function
Excel’s NORM.DIST and NORM.INV functions for analyzing normal distributions (bell curves)

WEEK 4
Distributions (Normal, Binomial, Poisson): Module 4
The Normal distribution is used in many contexts throughout this module. Additionally, the Binomial and Poisson distributions will be shown to you. Understanding the difference between data collected from a sample and data collected from a population is the setting in which the Central Limit Theorem is introduced and discussed.

Included are discussions on • Several contexts in which the Normal distribution is useful
Sample versus population data; the Central Limit Theorem; the Binomial and Poisson distributions

FACULTIES YOU WILL ACQUIRE

• Statistics
• Examining the Numbers
• Statistically, This Is a Normal Distribution
• Inverse Poisson Distribution

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