Question

Consider a standard normal random variable with μ = 0 and a standard deviation σ = 1. Find the following probabilities:

a) P (Z <2.9)
b) P (Z> 1.32)
c) P (-2.72 <Z <2.72)
d) P (Z <1.93)

Answer 1

Solution :

Given that ,

Using standard normal table,

a)

P(Z < 2.9) = 0.9981

Probability = 0.9981

b)

P(Z > 1.32) = 1 - P(Z < 1.32)

= 1 - 0.9066

= 0.0934

Probability = 0.0934

c)

P(-2.72 < z < 2.72)

= P(z < 2.72) - P(z < -2.72)

= 0.9967 - 0.0033

= 0.9934

Probability = 0.9934

d)

P(x < 1.93) = 0.9732

Probability = 0.9732