Question

​

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

3.0

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

66

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

66

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

66

and

70

inches.The probability that the study participant selected at random is between

66

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 event in part

left parenthesis a right parenthesis(a)

is unusual because its probability is less than 0.05.

B.

The events in parts left parenthesis a right parenthesis comma left parenthesis b right parenthesis comma and left parenthesis c right parenthesis are unusual because all of their probabilities areThe events in parts (a), (b), and (c) are unusual because all of their probabilities are  

lessless

than 0.05.

C.

There are no unusual events because all the probabilities are greaterThere are no unusual events because all the probabilities are greater

than 0.05.

D.

The events in parts

left parenthesis a right parenthesis and left parenthesis c right parenthesis(a) and (c)

are unusual because its probabilities are less than 0.05.

        More

                                                        Less

Answer 1

Mean, = 68.9 inches

Standard deviation, = 3.0 inches

Let X be a random variable which denotes the height of a participant (in inches)

(a) P(X < 66)

The corresponding z value = (66 - 68.9)/3 = -0.967

P(X < 66) = P(Z < -0.967) = 0.1669

(b) P( 66 <= X <= 70)

= P( -0.967 <= Z <= 0.367)

= 0.4762

(c) P(X > 70)

= P(Z > 0.367)

= 0.3569

(d) There are no unusual events because all the probabilities are greater than 0.05

Option (C)