The population of men at UMBC has a mean height of 69 inches with a standard deviation of 4 inches. The women at UMBC have a mean height of 65 inches with a standard deviation of 3 inches. A sample of 50 men and 40 women is selected. What is the probability that the sample mean of men heights is more than 5 inches greater than the sample mean of women heights

The probability that the sample mean of men heights is more than 5 inches greater than the sample mean of women heights is 0.0885.

Step-by-step explanation:

We are given that the population of men at UMBC has a mean height of 69 inches with a standard deviation of 4 inches. The women at UMBC have a mean height of 65 inches with a standard deviation of 3 inches.

A sample of 50 men and 40 women is selected.

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

                          Z  =    ~ N(0,1)

where, = population mean height of men at UMBC = 69 inches

            = population mean height of women at UMBC = 65 inches

            = standard deviation of men at UMBC = 4 inches

            = standard deviation of women at UMBC = 3 inches

            = sample of men = 50

            = sample of women = 40

Now, the probability that the sample mean of men heights is more than 5 inches greater than the sample mean of women heights is given by = P( > 5 inches)

 P( > 5 inches) = P( > ) = P(Z > 1.35)

                                         = 1 - P(Z 1.35) = 1 - 0.9115 = 0.0885

The above probability is calculated by looking at the value of x = 1.35 in the z table which has an area of 0.9115.      

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