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Step 3 (c) What mean weights (in pounds) for a sample of 16 people will result in the total weight exceeding the weight limit of 2,700 pounds? Since the elevator holds a maximum of 16 people and the average weight of each person is x, the weight capacity of 2,700 pounds will be exceeded when (16- 16 2 2,700. Step 4 We determined that the weight capacity is exceeded if 16x 2 2,700. In other words, if x 2 2700 ]× for a particular sample of 16 people, then the weight capacity will be exceeded.

Step 3 (c) What mean weights (in pounds) for a sample of 16 people will result in the total weight exceeding the weight limit of 2,700 pounds? Since the elevator holds a maximum of 16 people and the average weight of each person is x, the weight capacity of 2,700 pounds will be exceeded when (16- 16 2 2,700. Step 4 We determined that the weight capacity is exceeded if 16x 2 2,700. In other words, if x 2 2700 ]× for a particular sample of 16 people, then the weight capacity will be exceeded.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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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Step 1 (a) What is the mean of the sampling distribution of x? We are given that the average weight of students, faculty, and staff at a college is u = 165 pounds, that the standard deviation is a = 33 pounds, and that the distribution of weights of individuals on campus is approximately normal. We are asked to determine the mean for the sampling distribution of the sample mean, x, for a random sample of size n = 16. Recall the general property of the sampling distribution x: the mean is - = H. Therefore, - - 165 165 Step 2 (b) What is the standard deviation of the sampling distribution of x? Recall the general property of the sampling distribution x: the standard deviation is a- = We are given that the standard deviation is a = 33 pounds and the random sample has size n = 16. Use these values to calculate the mean for the sampling distribution of the sample mean. 33 33 16 33/4 8.25 Step 3 (c) What mean weights (in pounds) for a sample of 16 people will result in the total weight exceeding the weight limit of 2,700 pounds? Since the elevator holds a maximum of 16 people and the average weight of each person is x, the weight capacity of 2,700 pounds will be exceeded when (16 16 x2 2,700. iz2,700. Step 4 We determined that the weight capacity is exceeded if 16x 2 2,700. In other words, if x 2 2700 x for a particular sample of 16 people, then the weight capacity will be exceeded.
Transcribed Image Text:Step 1 (a) What is the mean of the sampling distribution of x? We are given that the average weight of students, faculty, and staff at a college is u = 165 pounds, that the standard deviation is a = 33 pounds, and that the distribution of weights of individuals on campus is approximately normal. We are asked to determine the mean for the sampling distribution of the sample mean, x, for a random sample of size n = 16. Recall the general property of the sampling distribution x: the mean is - = H. Therefore, - - 165 165 Step 2 (b) What is the standard deviation of the sampling distribution of x? Recall the general property of the sampling distribution x: the standard deviation is a- = We are given that the standard deviation is a = 33 pounds and the random sample has size n = 16. Use these values to calculate the mean for the sampling distribution of the sample mean. 33 33 16 33/4 8.25 Step 3 (c) What mean weights (in pounds) for a sample of 16 people will result in the total weight exceeding the weight limit of 2,700 pounds? Since the elevator holds a maximum of 16 people and the average weight of each person is x, the weight capacity of 2,700 pounds will be exceeded when (16 16 x2 2,700. iz2,700. Step 4 We determined that the weight capacity is exceeded if 16x 2 2,700. In other words, if x 2 2700 x for a particular sample of 16 people, then the weight capacity will be exceeded.
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