Question

In a survey of a group of men, the heights in the 20-29 age group were normally distributed, with a mean of 68.8 inches and a standard deviation of 20 inches. If a study participant is randomly selected from this age group, what is the probability that their height falls between 60 inches and 80 inches?

Answer 1

The probability that a randomly selected study participant's height falls between 60 inches and 80 inches is 38.04%.

Step-by-step explanation:

To find the probability that a randomly selected study participant's height falls between 60 inches and 80 inches, we need to find the area under the normal distribution curve between these two heights. Using the mean of 68.8 inches and the standard deviation of 20 inches, we can calculate the z-scores for both heights.

The z-score for 60 inches is calculated as (60 - 68.8) / 20 = -0.44. The z-score for 80 inches is calculated as (80 - 68.8) / 20 = 0.56. We can then use a standard normal distribution table or calculator to find the area under the curve between these z-scores.

For z = -0.44, the area to the left is 0.3319. For z = 0.56, the area to the left is 0.7123. Subtracting the area to the left for z = -0.44 from the area to the left for z = 0.56, we find the probability that the height falls between 60 inches and 80 inches is 0.7123 - 0.3319 = 0.3804, or 38.04%.