Answer to Question #275807 in Statistics and Probability for Gon

Question

Assume z is a normal random variable with mean 0 and standard deviation 1.

Answer 1

$Z\sim N(0,1)$

a)

$$P(-1.55<Z<1.86)$$

$$=P(Z<1.86)-P(Z\leq -1.55)$$

$$\approx0.9685572-0.0605708$$

$$\approx0.907986$$

b)

$$P(X<-1.55\ or\ x>1.86)$$

$$=1-P(-1.55<X<1.86)$$

$$\approx1-0.907986$$

$$\approx0.092014$$

c)

$$P(Z>z)=0.015$$

$$1-P(Z\leq z)=0.015$$

$$P(Z\leq z)=0.985$$

$$z\approx2.1701$$