In a survey of a group of? men, the heights in the? 20-29 age group were normall

Question

In a survey of a group of? men, the heights in the? 20-29 age group were normally? distributed, with a mean of 67.7 inches and a standard deviation of 2.0 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 nothing. ?(Round to four decimal places as? needed.) ?(b) Find the probability that a study participant has a height that is between 68 and 70 inches. The probability that the study participant selected at random is between 68 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 is unusual because its probability is less than 0.05. B. The events in parts left parenthesis a right parenthesis and left parenthesis c right parenthesis 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 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 are

Explanation / Answer

Sol:

mean=67.7

sd=20

solutionA:

P(X<68)

z=x-mean/sd

z=68-67.7/2

z=0.15

P(Z<0.15)

fro m standard normal table

=0.5596

ANSWER:0.5596

The probability that the study participant selected at random is less than 68 inches tall is nothing is 0.5596

SolutionB:

(b) Find the probability that a study participant has a height that is between 68 and 70 inches.

P(68<X<70)

P(68-67.7/2<Z<70-67.7/2)

P(0.15<Z<1.15)

=P(Z<1.15)-P(Z<0.15)

=0.8749-0.5596

=0.3153

ANSWER:0.3153

he probability that the study participant selected at random is between 68 and 70 inches tall is nothing

=0.3153

Solutionc:

P(X>70)

z=70-67.7/2

z=1.15

P(Z>1.15)

=1-P(Z<1.15)

=1-0.8749

=0.1251

ANSWER:0.1251

The probability that the study participant selected at random is more than 70 inches tall is nothing.

=0.1251

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

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