Question

fill in the blank 4 points
in a survey of a group of men, the heights in the 20 - 29 age group were normally distributed, with a mean of 69.2 inches and a standard deviation of 3.0 inches. a study participant is randomly selected. complete parts (a) through (d) below.
(a) the probability that the study participant selected at random is less than 66 inches tall is 0.1423 (round to four decimal places as needed.)
(b) the probability that the study participant selected at random is between 66 and 72 inches tall is 0.6813 (round to four decimal places as needed.)
(c) the probability that the study participant selected at random is more than 72 inches tall is 0.1762 (round to four decimal places as needed.)
(d) identify any unusual events. explain your reasoning. choose the correct answer below. d
a. the events in parts (a) and (c) are unusual because its probabilities are less than 0.05.
b. the event in part (a) is unusual because its probability is less than 0.05.
c. there are no unusual events because all the probabilities are greater than 0.05.
d. the events in parts (a), (b), and (c) are unusual because all of their probabilities are less than 0.05.

Explanation:

Step1: Recall the rule for unusual events

An event is considered unusual if its probability is less than \(0.05\).

Step2: Check the probabilities

In part (a), the probability is \(0.1423> 0.05\). In part (b), the probability is \(0.2813>0.05\). In part (c), the probability is \(0.1762>0.05\).

Answer:

C. There are no unusual events because all the probabilities are greater than \(0.05\)