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a. Calculate the probability that the average number of minutes that diners spend at their table for dinner will be less than 100 minutes using a sample size of 9 tables. (Round to three decimal places as needed.) b. Calculate the probability that the average number of minutes that diners spend at their table for dinner will be less than 100 minutes using a sample size of 21 tables. (Round to three decimal places as needed.) c. Calculate the probability that the average number of minutes that diners spend at their table for dinner will be less than 100 minutes using a sample size of 30 tables.

a. Calculate the probability that the average number of minutes that diners spend at their table for dinner will be less than 100 minutes using a sample size of 9 tables. (Round to three decimal places as needed.) b. Calculate the probability that the average number of minutes that diners spend at their table for dinner will be less than 100 minutes using a sample size of 21 tables. (Round to three decimal places as needed.) c. Calculate the probability that the average number of minutes that diners spend at their table for dinner will be less than 100 minutes using a sample size of 30 tables.

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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At a certain restaurant in Ohio, the number of minutes that diners spend at the table has a major impact on the profitability of the restaurant. Suppose the average number of minutes that diners spend at a table for dinner at the restaurant is 93 minutes with a standard deviation of 19 minutes. Assume the number of minutes diners spend at their table follows the normal probability distribution. Complete parts a through d. a. Calculate the probability that the average number of minutes that diners spend at their table for dinner will be less than 100 minutes using a sample size of 9 tables. (Round to three decimal places as needed.) b. Calculate the probability that the average number of minutes that diners spend at their table for dinner will be less than 100 minutes using a sample size of 21 tables. (Round to three decimal places as needed.) c. Calculate the probability that the average number of minutes that diners spend at their table for dinner will be less than 100 minutes using a sample size of 30 tables. (Round to three decimal places as needed.) d. Explain the difference in these probabilities. Choose the correct answer below. O A. With a larger sample size, the standard error of the mean increases and the sample means tend to move closer to the population mean of 93 seconds. Therefore, the probability of observing a sample mean less than 100 seconds increases as the sample size increases. O B. With a larger sample size, the standard error of the mean increases and the sample means tend to move further away from the population mean of 93 seconds. Therefore, the probability of observing a sample mean less than 100 seconds decreases as the sample size increases. Oc. With a larger sample size, the standard error of the mean stays the same and the sample means stay the same. Therefore, the probability of observing a sample mean less than 100 seconds decreases as the sample size increases. O D. With a larger sample size, the standard error of the mean decreases and the sample means tend to move closer to the population mean of 93 seconds. Therefore, the probability of observing a sample mean less than 100 seconds increases as the sample size increases.
Transcribed Image Text:At a certain restaurant in Ohio, the number of minutes that diners spend at the table has a major impact on the profitability of the restaurant. Suppose the average number of minutes that diners spend at a table for dinner at the restaurant is 93 minutes with a standard deviation of 19 minutes. Assume the number of minutes diners spend at their table follows the normal probability distribution. Complete parts a through d. a. Calculate the probability that the average number of minutes that diners spend at their table for dinner will be less than 100 minutes using a sample size of 9 tables. (Round to three decimal places as needed.) b. Calculate the probability that the average number of minutes that diners spend at their table for dinner will be less than 100 minutes using a sample size of 21 tables. (Round to three decimal places as needed.) c. Calculate the probability that the average number of minutes that diners spend at their table for dinner will be less than 100 minutes using a sample size of 30 tables. (Round to three decimal places as needed.) d. Explain the difference in these probabilities. Choose the correct answer below. O A. With a larger sample size, the standard error of the mean increases and the sample means tend to move closer to the population mean of 93 seconds. Therefore, the probability of observing a sample mean less than 100 seconds increases as the sample size increases. O B. With a larger sample size, the standard error of the mean increases and the sample means tend to move further away from the population mean of 93 seconds. Therefore, the probability of observing a sample mean less than 100 seconds decreases as the sample size increases. Oc. With a larger sample size, the standard error of the mean stays the same and the sample means stay the same. Therefore, the probability of observing a sample mean less than 100 seconds decreases as the sample size increases. O D. With a larger sample size, the standard error of the mean decreases and the sample means tend to move closer to the population mean of 93 seconds. Therefore, the probability of observing a sample mean less than 100 seconds increases as the sample size increases.
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