The distribution of heights of adult men in the U.S. is approximately normal wit

Question

The distribution of heights of adult men in the U.S. is approximately normal with mean 69 inches and standard deviation 2.5 inches. Use what you know about the EMPIRICAL RULE to answer the following. NOTE: If your answer is a percent, such as 25 percent, enter: "25 PERCENT" (without the quotes). If your answer is in inches, such as 10 inches, enter: "10 INCHES" (without the quotes and with a space between the number and the INCHES). If your answer is an interval, such as 14 to 15 inches, then enter: "14 TO 15 INCHES" (without the quotes). Do not use extra zeros and do not include a decimal point unless your answer is not a whole number. Your answer must be entered in the correct format.

QUESTION: Approximately what percent of men are between 69 and 74 inches?

Explanation / Answer

Solution:

P (69<X<74)=0.4772

=47.72%

Explanation:

Since =69 and =2.5 we have:

P ( 69<X<74 )=P ( 6969< X<7469 )

=P ( 6969/2.5<X/<7469/2.5)

Since Z=x/ , 6969/2.5=0 and 7469/2.5=2 we have:

P ( 69<X<74 )=P ( 0<Z<2 )

P (0<Z<2 )=P ( Z<2 )P (Z<0 )

P ( Z<2 ) can be found by using the following standard normal table

We see that P ( Z<2 )=0.9772

P ( Z<0 ) can be found by using the following standard normal table.

We see that  P ( Z<0 )=0.5

threfore P (0<Z<2 ) =0.9772-0.5

P (0<Z<2 ) =0.4772

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