In a survey of a group of men, the heights in the 20-29 age group were normally distributed, with a mean of 68.1 inches and a standard deviation of 2.0 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 68 inches.
The probability that the study participant selected at random is less than 68 inches tall is 4801 . (Round to four decimal places as needed.)
(b) Find the probability that a study participant has a height that is between 68 and 71 inches.
The probability that the study participant selected at random is between 68 and 71 inches tall is (Round to four decimal places as needed.)

Step 1 ：We are given that the heights are normally distributed with a mean of 68.1 inches and a standard deviation of 2.0 inches. We are asked to find the probability that a randomly selected participant has a height less than 68 inches and between 68 and 71 inches.

Step 2 ：To solve this, we can use the properties of the normal distribution. The probability that a random variable X is less than a certain value x is given by the cumulative distribution function (CDF) of the normal distribution, which is denoted by P(X < x).

Step 3 ：For part (a), we need to find P(X < 68). Since the heights are normally distributed, we can standardize the value 68 by subtracting the mean and dividing by the standard deviation to get the z-score. Then we can use the CDF of the standard normal distribution to find the probability.

Step 4 ：For part (b), we need to find P(68 < X < 71). We can find this by subtracting the CDF value at 68 from the CDF value at 71.

Step 5 ：Final Answer: The probability that a study participant selected at random is less than 68 inches tall is approximately \(\boxed{0.4801}\). The probability that the study participant selected at random is between 68 and 71 inches tall is approximately \(\boxed{0.4464}\).