In a survey of a group of men, the heights in the 20-29 age group were normally distributed, with a mean of 69.9 inches and a standard deviation of 4.0 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 65 inches. The probability that the study participant selected at random is less than 65 inches tall is nothing. (Round to four decimal places as needed.)

The probability that a study participant has a height that is less than 65 inches is 0.1103.

Step-by-step explanation:

We are given that the heights in the 20-29 age group were normally distributed, with a mean of 69.9 inches and a standard deviation of 4.0 inches.

A study participant is randomly selected.

Let X = heights in the 20-29 age group.

So, X ~ Normal()

The z-score probability distribution for the normal distribution is given by;

                             Z  =    ~ N(0,1)

where, = mean height = 69.9 inches

            = standard deviation = 4.0 inches

Now, the probability that a study participant has a height that is less than 65 inches is given by = P(X < 65 inches)

      P(X < 65 inches) = P( < ) = P(Z < -1.225) = P(Z 1.225)

                                                                 =  1 - 0.8897 = 0.1103

The above probability is calculated by looking at the value of x = 1.225 in the z table which lies between x = 1.22 and x = 1.23 which has an area of 0.88877 and 0.89065 respectively.