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## In a survey of a group of​ men, the heights in the​ 20-29 age group were normally​ distributed, with a mean of 67.9 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 67 inches.   The probability that the study participant selected at random is less than 67 inches tall is nothing. ​(Round to four decimal places as​ needed.) ​(b) Find the probability that a study participant has a height that is between 67 and 70 inches.   The probability that the study participant selected at random is between 67 and 70 inches tall is nothing. ​(Round to four decimal places as​ needed.) ​(c) Find the probability that a study participant has a height that is more than 70 inches.   The probability that the study participant selected at random is more than 70 inches tall is nothing. ​(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. The events in parts (a) and (c) are unusual because its probabilities are less than 0.05.   C. There are no unusual events because all the probabilities are greater than 0.05.   D. The event in part (a) is unusual because its probability is less than 0.05.

In a survey of a group of​ men, the heights in the​ 20-29 age group were normally​ distributed, with a mean of

67.9

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

67

inches.

The probability that the study participant selected at random is less than

67

inches tall is

nothing.

​(Round to four decimal places as​ needed.)

​(b) Find the probability that a study participant has a height that is between

67

and

70

inches.

The probability that the study participant selected at random is between

67

and

70

inches tall is

nothing.

​(Round to four decimal places as​ needed.)

​(c) Find the probability that a study participant has a height that is more than

70

inches.

The probability that the study participant selected at random is more than

70

inches tall is

nothing.

​(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.

The events in parts

(a) and (c)

are unusual because its probabilities are less than 0.05.

C.

There are no unusual events because all the probabilities are greater

than 0.05.

D.

The event in part

(a)

is unusual because its probability is less than 0.05.

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