Question

Assume that the monthly rainfall in New York is normally distributed with mean 35.4 inches and standard deviation 4.2 inches. A research is conducted at the university of Ottawa for 10 months. Let D = X1 − X10 be the difference of the rainfall in month 1 and in month 10. Compute the mean and the standard deviation of D, respectively. Assume that monthly rainfall are independent.

A.0; 8.4 B.0; 5.9 C.0; 0 D.-35.4; 5.9 E.-35.4; 8.4

Answer 1

[#demotes number of Leandem has PAGE NO.: DATE: whe Given that monthly ranfall is normally distributed with mean 35.4 inch & standard deviation 4.2 inch. O=xi-xi whore Xi is the ramfall for the th month. Moreover, it is said that the monthly rainfall are independent lid So, X, Xio N (35.4 inch, 4.2² inches . 2 So, D=X - Xro Meam = E(D)- E(X.) - Elxio) = 0 ved Variance (0) Var (X.) + Var(x,0) - 2 cov(x, xro) Van (x) + Vas (x,0) [cov Cx, wko) = 0 asx,,kio are 4.22 +4.22 independent C 30 35.28 Standard deviations Variance (D) = 65.94 ~ 5.9 So, o has mean ol standard deviation 5.9 11 Hence opton B is correct. CMS anagar Parent's Signature berenangan