Question

) Find the following probabilities for the standard normal random variable zz:

(a)  P(−2≤z≤2.01)=

(b)  P(−0.5≤z≤1.62)=

(c)  P(z≤1.3)=

(d)  P(z>−1.1)=

Answer 1

Here we need to find the probabilities for the standard normal random variable.

Before we go on to solve the problem let us know a bit about standard normal distribution.

A continuous random variable Z is said to have a standard normal distribution if its PDF (Probability Density Function) is given by,

Coming back to our problem

(a) Here we need to find P(−2 ≤ Z ≤ 2.01),

(b) Here we need to find P(−0.5 ≤ Z ≤ 1.62),

(c) Here we need to find P(Z ≤ 1.3),

(d) Here we need to find P(Z > −1.1)