Question

Heights of adult men have an appropriately normal distribution. The mean height for adult men in the U.S is 5ft 10 inches with a standard deviation of 4 inches. What is the range of heights for the middle 75% of adult men in the U.S?

a) 5ft⁶ inches to 6ft² inches
b) 5ft⁴ inches to 6ft⁴ inches
c) 5ft⁷ inches to 6ft¹ inch
d) 5ft⁵ inches to 6ft³ inches

Answer 1

The range of heights for the middle 75% of adult men in the U.S. is approximately 67.3 inches to 72.7 inches.

Step-by-step explanation:

To find the range of heights for the middle 75% of adult men in the U.S., we need to find the z-scores corresponding to the 25th and 75th percentiles.

Using the formula z = (x - mean) / standard deviation, we can calculate the z-scores.

The z-score corresponding to the 25th percentile is -0.674. Using the formula x = z * standard deviation + mean, we can find the corresponding height: x = -0.674 * 4 + 70 = approximately 67.3 inches.

The z-score corresponding to the 75th percentile is 0.674. Using the same formula, we can find the corresponding height: x = 0.674 * 4 + 70 = approximately 72.7 inches.

Therefore, the range of heights for the middle 75% of adult men in the U.S. is approximately 67.3 inches to 72.7 inches.