# Normal Random Variables Question

#### Onetimeuser

1. Homework Statement

Problem 1 – Normal Random Variables

B) Y ~ N(300, 100). Pr (300 < Y < 320) = 0.4772

D) H ~ N(4000, 25). R = f(H) = 0.5H – 60. E(R) = 1940; Var(R) = 156.25

I have a problem solving these problems above...I missed the class when we covered this subject and now I am lost upon solving them.. I hope somebody can help, thanks a lot

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#### statdad

Homework Helper
For a normally distributed random variable,

$$P(a < X < b) = P(X < b) - P(X < a)$$

For any random variable $W$, if $a, b$ are real numbers,
and

$$Z = aW + b$$

then

$$E(Z) = aE(W) + b, \quad Var(Z) = a^2 Var(W)$$

(as long as the mean and variance of $W$ exist)

#### Onetimeuser

Thanks for the reply!!

However, when I plug it in I dnt get the right answer.... did u check if the given answer is right?

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