Question

Given that z is a standard normal random variable, find z for each situation (to 2 decimals).

a. The area between -z and z is 0.2206 .
b. The area to the left of z is 0.9951 .

Answer 1

Explanation:

a. The area between -z and z is 0.2206, so we want to find the value of z such that P(-z < Z < z) = 0.2206.

The standard normal distribution is symmetric, so P(-z < Z < z) = 0.5 - P(Z < -z) = 0.5 - P(Z < -z) = 0.5 - 0.2206 = 0.2794

We can use a standard normal table to find the z-value such that P(Z < z) = 0.2794 which is z = 0.68.

b. The area to the left of z is 0.9951, so we want to find the value of z such that P(Z < z) = 0.9951.

We can use a standard normal table to find the z-value such that P(Z < z) = 0.9951 which is z = 2.33.