In a survey of a group of men, the heights in the 20-29 age group were normally distributed, with a mean of 67.2 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 67 inches. The probability that the study participant selected at random is less than 67 inches tall is \( \square \). (Round to four decimal places as needed.)

To find the probability that a study participant has a height less than 67 inches, we can use the Z-score formula. First, we find the Z-score using the formula: \[ Z = \frac{(X - \mu)}{\sigma} \] where \( X \) is the height (67 inches), \( \mu \) is the mean (67.2 inches), and \( \sigma \) is the standard deviation (2.0 inches). Calculating the Z-score: \[ Z = \frac{(67 - 67.2)}{2.0} = \frac{-0.2}{2.0} = -0.1 \] Next, we can look up this Z-score in a standard normal distribution table, or use a calculator or software that provides cumulative distribution function values for normal distributions. The cumulative probability for \( Z = -0.1 \) gives us approximately 0.4602. Thus, the probability that the study participant selected at random is less than 67 inches tall is \( 0.4602 \). **Answer:** The probability that the study participant selected at random is less than 67 inches tall is \( 0.4602 \) (rounded to four decimal places).