11. The male heights are normally distributed with a mean of 170 cmand a varianc

Question

11. The male heights are normally distributed with a mean of 170 cmand a variance of 102 cm. The female heights are also normally distributed with a mean of 160 cm and a variance of 102 cm2. You randomly select one male student and one female student. Let X denote the male student's height, and let Y denote the female student's height. Which of the following is correctly stated? a. X-Y is normally distributed with a mean of 10 and variance of 2'102 X-Yis normally distributed with a mean of 10 and variance of V2*10 X-Y is not normally distributed with a mean of 165 and variance of 2*102 c. X-Y is normally distributed with a mean of 165 and variance ofV2*10 5 pts) 12. Refer to Problem 11, what is the probability that the male student is taller than the female student, P(X>Y)? z.S 241 .Iss

Explanation / Answer

Male:

x1 = 170

s1^2 = 100

s1 = 10

Female:

x2 = 160

s2^2 = 100

s2 = 10

X-Y is also normal

E[X-Y] = E[X] - E[Y] = 170-160 = 10

V[X-Y] =V[X^2] + V[Y^2] -2*Cov[X,Y] = 100+100-0 = 200= 2*10^2

That will be Option- (A)

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