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)

$P(Z>z)=0.015$

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

$P(Z\leq z)=0.985$

$z\approx2.1701$