A geneticist took a large sample of adults and measured their heights. Summary statistics for the heights of the men and women in the study are shown in the table below.
Suppose that we choose a random man and a random woman from the study and look at the difference between their heights. We can assume that their heights are independent. Let MMM represent the man's height, WWW represent the woman's height, and DDD represent the difference between their heights (D=M-W)(D=M−W)left parenthesis, D, equals, M, minus, W, right parenthesis.
Mean Standard deviation
Men \mu_M=175\,\text{cm}μ
M
=175cmmu, start subscript, M, end subscript, equals, 175, start text, c, m, end text \sigma_M=8\,\text{cm}σ
M
=8cmsigma, start subscript, M, end subscript, equals, 8, start text, c, m, end text
Women \mu_W=162\,\text{cm}μ
W
=162cmmu, start subscript, W, end subscript, equals, 162, start text, c, m, end text \sigma_W=7\,\text{cm}σ
W
=7cmsigma, start subscript, W, end subscript, equals, 7, start text, c, m, end text
Find the mean of DDD.
\mu_D=μ
D
=mu, start subscript, D, end subscript, equals
\text{cm}cmstart text, c, m, end text