Math  /  Data & Statistics

QuestionQuestion 4 1 pts
Provide an appropriate response.
If an adult male is told that his height is within 2 standard deviations of the mean of the normal distribution of heights of adult males, what can he assume? He is taller than about 95\% of the other men whose heights were measured. His height measurement is in the same range as about 99.7%99.7 \% of the other adult males whose heights were measured. He is taller than about 99.7\% of the other men whose heights were measured. His height measurement is in the same range as about 95\% of the other adult males whose heights were measured.

Studdy Solution

STEP 1

1. The distribution of adult male heights is normal.
2. The empirical rule (68-95-99.7 rule) applies to normal distributions.

STEP 2

1. Review the empirical rule for normal distributions.
2. Determine the correct interpretation of being within 2 standard deviations of the mean.

STEP 3

According to the empirical rule, for a normal distribution: - Approximately 68% of the data falls within 1 standard deviation of the mean. - Approximately 95% of the data falls within 2 standard deviations of the mean. - Approximately 99.7% of the data falls within 3 standard deviations of the mean.

STEP 4

If an adult male's height is within 2 standard deviations of the mean, it means his height falls within the range that includes about 95% of the population.
The correct interpretation is: His height measurement is in the same range as about 95% of the other adult males whose heights were measured.

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