HAWKES LEARNING SYSTEMS math courseware specialists Copyright 2008
- Slides: 14
HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2008 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 7. 2 Central Limit Theorem with Population Means
HAWKES LEARNING SYSTEMS math courseware specialists Sampling Distributions 7. 2 Central Limit Theorem with Population Means z-Score: • The z-score formula for population means becomes or Std Error Converting to the Standard Normal Curve:
HAWKES LEARNING SYSTEMS math courseware specialists Sampling Distributions 7. 2 Central Limit Theorem with Population Means Calculate the probability: The body temperatures of adults are normally distributed with a mean of 98. 6° F and a standard deviation of 0. 73° F. What is the probability of a sample of 36 adults having an average normal body temperature less than 98. 3° F? Solution: m = 98. 6, s = 0. 73, n = 36, = 98. 3 P(z < -2. 47) = 0. 0068
HAWKES LEARNING SYSTEMS math courseware specialists Sampling Distributions 7. 2 Central Limit Theorem with Population Means Calculate the probability: The body temperatures of adults are normally distributed with a mean of 98. 6° F and a standard deviation of 0. 73° F. What is the probability of a sample of 40 adults having an average normal body temperature greater than 99° F? Solution: m = 98. 6, s = 0. 73, n = 40, = 99 P(z > 3. 47) = 0. 0003
HAWKES LEARNING SYSTEMS math courseware specialists Sampling Distributions 7. 2 Central Limit Theorem with Population Means Calculate the probability: The body temperatures of adults are normally distributed with a mean of 98. 6° F and a standard deviation of 0. 73° F. What is the probability of a sample of 81 adults having an average normal body temperature that differs from the population mean by less than 0. 1° F? Solution: - m = 0. 1, s = 0. 73, n = 81 P(-1. 23 < z < 1. 23) = 0. 7824 P(98. 5 < X < 98. 7) = 0. 7824
HAWKES LEARNING SYSTEMS math courseware specialists Sampling Distributions 7. 2 Central Limit Theorem with Population Means Calculate the probability: The body temperatures of adults are normally distributed with a mean of 98. 6° F and a standard deviation of 0. 73° F. What is the probability of a sample of 100 adults having an average normal body temperature that differs from the population mean by more than 0. 05° F? Solution: - m = 0. 05, s = 0. 73, n = 100 P(z < -0. 68 or z > 0. 68) = 0. 4934 P(X < 98. 55 or X > 98. 65) = 0. 4934
