\( 1< \) In a survey of a group of men, the heights in the 20-29 age group were normally distributed, with a mean of 69.3 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 66 inches. The probability that the study participant selected at random is less than 66 inches tall is . (Round to four decimal places as needed.)

To solve for the probability that a randomly selected study participant has a height of less than 66 inches, we first calculate the z-score for 66 inches using the formula: \[ z = \frac{(X - \mu)}{\sigma} \] where: - \(X\) is the value we are evaluating (66 inches), - \(\mu\) is the mean height (69.3 inches), - \(\sigma\) is the standard deviation (2.0 inches). Calculating the z-score: \[ z = \frac{(66 - 69.3)}{2.0} = \frac{-3.3}{2.0} = -1.65 \] Now, we can find the probability corresponding to a z-score of -1.65 using the standard normal distribution table or a calculator. Looking up \(z = -1.65\) gives us a cumulative probability of approximately 0.0495. Thus, the probability that a study participant has a height less than 66 inches is: \[ \text{P(X < 66)} = 0.0495 \] Rounded to four decimal places, the answer is: \[ \text{P(X < 66)} \approx 0.0495 \]