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 95 minutes with a standard deviation of 17 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 90 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 90 minutes using a sample size of 20 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 90 minutes using a sample size of 28 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 95 seconds. Therefore, the probability of observing a sample mean less than 90 seconds decreases as the sample size increases. O B. 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 95 seconds. Therefore, the probability of observing a sample mean less than 90 seconds decreases as the sample size increases. O C. 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 95 seconds. Therefore, the probability of observing a sample mean less than 90 seconds decreases as the sample size increases. O D. 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 90 seconds decreases as the sample size increases.

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 95 minutes with a standard deviation of 17 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 90 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 90 minutes using a sample size of 20 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 90 minutes using a sample size of 28 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 95 seconds. Therefore, the probability of observing a sample mean less than 90 seconds decreases as the sample size increases. O B. 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 95 seconds. Therefore, the probability of observing a sample mean less than 90 seconds decreases as the sample size increases. O C. 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 95 seconds. Therefore, the probability of observing a sample mean less than 90 seconds decreases as the sample size increases. O D. 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 90 seconds decreases as the sample size increases.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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