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$131.3600. g. For part e) and f), is the assumption of normal necessary? O NoO Yes h. The owner of Don Mcalds gives a coupon for a free sundae to the 2% of all groups of 16 people who spend the most money. At least how much must a group of 16 spend in total to get the free sundae? $

$131.3600. g. For part e) and f), is the assumption of normal necessary? O NoO Yes h. The owner of Don Mcalds gives a coupon for a free sundae to the 2% of all groups of 16 people who spend the most money. At least how much must a group of 16 spend in total to get the free sundae? $

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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please answer the last 2 parts (g. and h.)

## Educational Exercise: Analyzing Spending at Don Mcalds ### Average Spending Analysis The average amount of money that people spend at Don Mcalds fast food place is $7.6400 with a standard deviation of $1.6800. We randomly select 16 customers and analyze their spending based on a normal distribution. Please answer the following questions, rounding all answers to four decimal places where applicable. #### Questions a. **Distribution of Individual Spending (X):** - \( X \sim N(\, \boxed{7.6400} \,, \boxed{1.6800} \, ) \) b. **Distribution of Average Spending (\(\bar{x}\)):** - \( \bar{x} \sim N(\, \boxed{7.6400} \,, \boxed{0.4200} \, ) \) c. **Distribution of Total Spending (\(\sum x\)):** - \( \sum x \sim N(\, \boxed{122.2400} \,, \boxed{6.7200} \, ) \) #### Probabilities d. **Probability of One Customer Spending More Than $8.2100:** - Probability: \(\boxed{0.3611}\) e. **Probability of 16 Customers Having an Average Spend Less Than $8.2100:** - Probability: \(\boxed{0.8944}\) f. **Probability of 16 Customers Spending More Than $131.3600:** - Probability: \(\boxed{0.0161}\) g. **Normal Assumption for Parts e) and f):** - Is the assumption of normal necessary? \(\boxed{\text{Yes}}\) #### Special Offer h. **Free Sundae Offer:** - The owner of Don Mcalds provides a coupon for a free sundae to the top 2% of all groups of 16 people who spend the most money. **Minimum Amount a Group Must Spend for a Free Sundae:** - Amount: \(\boxed{129.6040}\) Explore these concepts by calculating and interpreting the probabilities and distributions for better insight into consumer behavior in statistical contexts.
Transcribed Image Text:## Educational Exercise: Analyzing Spending at Don Mcalds ### Average Spending Analysis The average amount of money that people spend at Don Mcalds fast food place is $7.6400 with a standard deviation of $1.6800. We randomly select 16 customers and analyze their spending based on a normal distribution. Please answer the following questions, rounding all answers to four decimal places where applicable. #### Questions a. **Distribution of Individual Spending (X):** - \( X \sim N(\, \boxed{7.6400} \,, \boxed{1.6800} \, ) \) b. **Distribution of Average Spending (\(\bar{x}\)):** - \( \bar{x} \sim N(\, \boxed{7.6400} \,, \boxed{0.4200} \, ) \) c. **Distribution of Total Spending (\(\sum x\)):** - \( \sum x \sim N(\, \boxed{122.2400} \,, \boxed{6.7200} \, ) \) #### Probabilities d. **Probability of One Customer Spending More Than $8.2100:** - Probability: \(\boxed{0.3611}\) e. **Probability of 16 Customers Having an Average Spend Less Than $8.2100:** - Probability: \(\boxed{0.8944}\) f. **Probability of 16 Customers Spending More Than $131.3600:** - Probability: \(\boxed{0.0161}\) g. **Normal Assumption for Parts e) and f):** - Is the assumption of normal necessary? \(\boxed{\text{Yes}}\) #### Special Offer h. **Free Sundae Offer:** - The owner of Don Mcalds provides a coupon for a free sundae to the top 2% of all groups of 16 people who spend the most money. **Minimum Amount a Group Must Spend for a Free Sundae:** - Amount: \(\boxed{129.6040}\) Explore these concepts by calculating and interpreting the probabilities and distributions for better insight into consumer behavior in statistical contexts.
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