Question

The mean height of adult males is 72 inches, with a standard deviation of 2,5 inches. Consider the heights to follow a normal distribution. A. If a man is 71 inches tall, in what percentile does he lie? B. What percentage of men will be between 71 and 75 inches tall? C. How tall must a man be in the 98th percentile?

Answer 1

A man who is 71 inches tall would lie below the 50th percentile. The percentage of men between 71 and 75 inches tall can be found by calculating the area under the normal curve between the z-scores corresponding to these heights. The height for the 98th percentile can be determined by finding the z-score of the 98th percentile and using it to calculate the corresponding height.

Step-by-step explanation:

The mean height of adult males is 72 inches, with a standard deviation of 2.5 inches, and the heights follow a normal distribution.

1. To determine in what percentile a 71-inch tall man lies, we calculate the z-score and then refer to a standard normal distribution table or use a calculator that provides percentile information based on z-scores.
2. To find the percentage of men between 71 and 75 inches tall, we calculate the z-scores for both heights and find the area between them on the normal distribution curve.
3. To determine the height corresponding to the 98th percentile, we look for the z-score associated with the 98th percentile and then apply the z-score formula in reverse to find the corresponding height.