Question

in a survey of a group of men, the heights in the 20 - 29 age group were normally distributed, with a mean of 69.7 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 68 inches.
the probability that the study participant selected at random is less than 68 inches tall is 0.3352. (round to four decimal places as needed.)
(b) find the probability that a study participant has a height that is between 68 and 72 inches.
the probability that the study participant selected at random is between 68 and 72 inches tall is 0.3825. (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 inches tall is 0.2823. (round to four decimal places as needed.)
(d) identify any unusual events. explain your reasoning. choose the correct answer below.
a. the events in parts (a), (b), and (c) are unusual because all of their probabilities are less than 0.05.
b. there are no unusual events because all the probabilities are greater than 0.05.
c. the event in part (a) is unusual because its probability is less than 0.05.
d. the events in parts (a) and (c) are unusual because its probabilities are less than 0.05

Explanation:

Step1: Recall the definition of unusual events

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

Step2: Analyze the probabilities in parts (a), (b) and (c)

In part (a), the probability is 0.3352. In part (b), the probability is 0.3825. In part (c), the probability is 0.2823. All these probabilities are greater than 0.05.

Answer:

B. There are no unusual events because all the probabilities are greater than 0.05.