Question

(1 point) The distribution of heights of adult men in the U.S. is approximately normal with mean 69 inches and standarddeviation 2.5 inches. Use what you know about a normal distribution and the Empirical rule to answer the following.NOTE: If your answer is a percent, such as 25 percent, enter: "25 PERCENT" (without the quotes). If your answer is in inches,such as 10 inches, enter: "10 INCHES" (without the quotes and with a space between the number and the INCHES). If youranswer is an interval, such as 14 to 15 inches, then enter: "14 TO 15 INCHES" (without the quotes). Do not use extra zerosand do not include a decimal point unless your answer is not a whole number. Your answer must be entered in the correctformat.a) Between what approximate heights do the middle 95 percent of men fall?Answer:

Answer 1

Part a)

The mean height is 69 inches with a standard deviation of 2.5 inches.

If we consider a interval of heights that relies on no more than two standard deviations from the mean, we will cover, approximatelly, 95% of men's heights. Then, we interval that we're looking for is:

Answer: 64 TO 74 INCHES

Part b)

Since [69,74] is half of the interval in the previous answer, we might expect half of 95% as the percentage of men who are in this interval. That is:

Answer: 47.5 PERCENT

Part c)

A interval of heights that relies on no more than one standard deviation from the mean covers, approximatelly, 68% of men's heights. Then, we can consider that the percentage of men that are between 64 and 66.5 inches is given by 47.5 - 68/2 = 13.5.

Answr: 13.5 PERCENT