My question is on statistics

Question

In a survey of a group of​ men, the heights in the​ 20-29 age group were normally​ distributed, with a mean of 67.3 inches and a standard deviation of 4.0 inches. A study participant is randomly selected. Complete parts​ (a) through​ (d) below.

Find the probability that a study participant has a height that is less than

68

inches.

Find the probability that a study participant has a height that is between

68

and

70

inches.

Find the probability that a study participant has a height that is more than

70

inches.

Answer 1

Thank you Ms. Darlene!!!!

Prob ( x < 68) =

Prob ( z < (68-67.3)/4 ) = <-- changes to z-score

Prob ( z < 0.175) =

0.56946 <--- per the Normal Bell Curve table

==============================

Prob ( 68 < x < 70) =

Prob( x < 70) - Prob(x<68) =

Prob( z < (70-67.3)/4) - Prob(x < 68) =

Prob( z < 0.675) - Prob(z < 0.175) =

0.750162 - 0.56946 = 0.180702

============================================

Prob(z > 70) =

1 - Prob(z<70) =

1 - 0.750162 =

0.249838 < 25%