Concept explainers
Tocalculate:The probability that 75% or more of the women in the sample have been on a diet.
Answer to Problem 39E
The required probability is 0.0375.
Explanation of Solution
Given information:
Number of SRS = 267
Proportion of women which have been on a diet within the past 12 months = 70%
Formula used:
The mean of the sampling distribution of
The standard deviation of the sampling distribution of
Consider the proportion of women which have been on a diet within the past 12 months be p and proportion of women in the sample which have been on a diet be
So, we can write:
For the mean of the sampling distribution of
Substitute 0.70 for p in the formula
For the standard deviation of the sampling distribution, use the formula
Substitute 0.70 for p and 267 for n in the above formula and simplify.
Now, find the z-score by using the formula
Substitute 0.75 for
Find the probability by using table A.
Hence, the required probability is 0.0375.
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