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 0.165 . (Round to four decimal places as needed.) (b) Find the probability that a study participant has a height that is between 65 and 72 inches. The probability that the study participant selected at random is between 65 and 72 inches tall is 0.6160 . (Round to four decimal places as needed.) (c) Find the probability that a study participant has a height that is more than 72 inches. The probability that the study participant selected at random is more than 72 in hes tall is $\square$. (Round to four decimal places as needed.)
Solution
Step 1 ：The problem is asking for the probability that a study participant has a height that is more than 72 inches. This is a problem of normal distribution. We know that the mean height is 68.9 inches and the standard deviation is 4.0 inches.
Step 2 ：We can use the z-score formula to find the z-score for 72 inches, which is \((72-68.9)/4.0\).
Step 3 ：Then we can use the standard normal distribution table or a function to find the probability that a z-score is more than the calculated z-score.
Step 4 ：The probability that a z-score is more than a certain value is 1 minus the probability that the z-score is less than or equal to that value.
Step 5 ：Final Answer: The probability that the study participant selected at random is more than 72 inches tall is \(\boxed{0.2192}\). (Rounded to four decimal places as needed.)
