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Step 4 We determined that the weight capacity is exceeded if 16x ≥ 2,700. In other words, if x 2165 for a particular sample of 16 people, then the weight capacity will be exceeded.

Step 4 We determined that the weight capacity is exceeded if 16x ≥ 2,700. In other words, if x 2165 for a particular sample of 16 people, then the weight capacity will be exceeded.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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(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 μ = 165 pounds, that the standard deviation is o = 31 pounds, and that the distribution of weights of individuals on cam 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 μ = μ. Therefore, μ Step 2 (b) What is the standard deviation of the sampling distribution of X? σ- Recall the general property of the sampling distribution X: the standard deviation is distribution of the sample mean. σ- = Step 3 31 ✔ V 16 7.75✔ 31 7.75 0 √n 165✔ Step 4 We determined that the weight capacity is exceeded if 16x ≥ 2,700. In other words, if X > 165 165 We are given that the standard deviation is o = 31 pounds and the random sample has size n = 16. Use th (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 X for a particular sample of 16 people, then the weight capacity will be exceeded. 16 > 2,700.
Transcribed Image Text:(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 μ = 165 pounds, that the standard deviation is o = 31 pounds, and that the distribution of weights of individuals on cam 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 μ = μ. Therefore, μ Step 2 (b) What is the standard deviation of the sampling distribution of X? σ- Recall the general property of the sampling distribution X: the standard deviation is distribution of the sample mean. σ- = Step 3 31 ✔ V 16 7.75✔ 31 7.75 0 √n 165✔ Step 4 We determined that the weight capacity is exceeded if 16x ≥ 2,700. In other words, if X > 165 165 We are given that the standard deviation is o = 31 pounds and the random sample has size n = 16. Use th (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 X for a particular sample of 16 people, then the weight capacity will be exceeded. 16 > 2,700.
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