Question

In a survey of a group of men, the heights in the 20-29 age group were normally distributed, with a mean of 69.7 inches and a standard deviation of 4.0 inches. A study participant is randomly selected. Complete parts (a) through (d) below.

(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

Answer 1

Mean = = 69.7

Standard deviation = = 4

We have to find the probability that a study participant has a height that is between 68 and 70 inches.

That is we have to find P( 68 < X < 70)

For finding this probability we have to find z score.

That is we have to find P( - 0.43 < Z < 0.07)

P( - 0.43 < Z < 0.07) = P(Z < 0.07) - P(Z < - 0.43) = 0.5279 - 0.3336 = 0.1943

( Using z table)

The probability that the study participant selected at random is between 68 and 70 inches tall is 0.1943