Q. 39 - The Practice of Statistics for AP | StudyQuestionHub

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Q. 39

Question

Students on diets A sample survey interviews an SRS of $267$ college women. Suppose (as is roughly true) that $70 %$ of college women have been on a diet within the past $12$ months. What is the probability that $75 %$ or more of the women in the sample have been on a diet? Follow the four-step process.

Step-by-Step Solution

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Answer

The probability that $75 %$ or more of the women in the sample have been on a diet is $0.0375 .$

1Step 1: Given Information

Number of $S R S = 267$

The proportion of women on a diet within the past $12$ months $= 70 %$

2Step 2: Explanation

We have,

$p = 70 % = 0.70$

$\hat{p} = 75 % = 0.75$

$n = 267$

$\hat{p}$ is equal to the percentage of the population $p$ in the sampling distribution:

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