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Section 7.2
Central Limit Theorem with Population Means
HAWKES LEARNING SYSTEMS
math courseware specialists
Copyright © 2008 by Hawkes Learning
Systems/Quant Systems, Inc.
All rights reserved.
• The z-score formula for population means becomes
HAWKES LEARNING SYSTEMS
math courseware specialists
z-Score:
Sampling Distributions
7.2 Central Limit Theorem with
Population Means
or
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?
Calculate the probability:
HAWKES LEARNING SYSTEMS
math courseware specialists
98.6,0.73, n 36, 98.3
Solution:
Sampling Distributions
7.2 Central Limit Theorem with
Population Means
P(z < 2.47) 0.0068
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?
Calculate the probability:
HAWKES LEARNING SYSTEMS
math courseware specialists
98.6,0.73, n 40, 99
Solution:
Sampling Distributions
7.2 Central Limit Theorem with
Population Means
P(z > 3.47) 0.0003
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?
Calculate the probability:
HAWKES LEARNING SYSTEMS
math courseware specialists
0.01,0.73, n 81
Solution:
Sampling Distributions
7.2 Central Limit Theorem with
Population Means
P(1.23 < z < 1.23) 0.7814
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?
Calculate the probability:
HAWKES LEARNING SYSTEMS
math courseware specialists
0.05,0.73, n 100
Solution:
Sampling Distributions
7.2 Central Limit Theorem with
Population Means
P(z < 0.68 or z > 0.68) 0.4966
