In a survey of a group of men, the heights in the 20-29 age group were normally distributed, with a mean of 68.9 inches and a standard deviation of 4.0 inches. A study participant is randomly selected. Complete parts (a) through (d) below. (a) Find the probability that a study participant has a height that is less than 65 inches. The probability that the study participant selected at random is less than 65 inches tall is (Round to four decimal places as needed.)

Step 1 ：The problem is asking for the probability that a randomly selected participant from the study has a height less than 65 inches. This is a problem of normal distribution.

Step 2 ：The formula for calculating the z-score is: \(z = \frac{X - \mu}{\sigma}\) where: \(X\) is the value we are interested in (in this case, 65 inches), \(\mu\) is the mean (in this case, 68.9 inches), and \(\sigma\) is the standard deviation (in this case, 4.0 inches).

Step 3 ：Once we have the z-score, we can use a z-table or a statistical function to find the probability that a randomly selected participant has a height less than 65 inches.

Step 4 ：Substituting the given values into the z-score formula, we get: \(z = \frac{65 - 68.9}{4.0} = -0.975\)

Step 5 ：Using a z-table or a statistical function, we find that the probability corresponding to a z-score of -0.975 is approximately 0.165.

Step 6 ：This means that there is a 16.5% chance that a randomly selected participant from the study has a height less than 65 inches.

Step 7 ：Final Answer: The probability that a study participant selected at random is less than 65 inches tall is approximately \(\boxed{0.165}\).