Question

question
in an all boys school, the heights of the student body are normally distributed with a mean of 69 inches and a standard deviation of 2.5 inches. using the empirical rule, determine the interval of heights that represents the middle 99.7% of male heights from this school.
answer
attempt 1 out of 2
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Explanation:

Step1: Recall Empirical Rule for 99.7%

For normal distribution, 99.7% data lies within \( \mu \pm 3\sigma \), where \( \mu \) is mean, \( \sigma \) is standard deviation.
Given \( \mu = 69 \), \( \sigma = 2.5 \).

Step2: Calculate Lower Bound

Lower bound: \( \mu - 3\sigma = 69 - 3\times2.5 = 69 - 7.5 = 61.5 \).

Step3: Calculate Upper Bound

Upper bound: \( \mu + 3\sigma = 69 + 3\times2.5 = 69 + 7.5 = 76.5 \).

Answer:

\((61.5, 76.5)\)