Question

1.For a standard normal distribution, find:P(1.26 < z < 1.48)2.For a standard normal distribution, given:P(z < c) = 0.1288

Answer 1

Standard Normal Distribution

To find the cumulative probability of a Normal Distribution, we need to use some automated digital tool that makes the calculations for us, since it's a pretty complex formula.

We'll use an online tool and provide the results here.

a) P(1.26 < z < 1.48)

The procedure is: Find P(z < 1.48) directly from the tool. Find P(z < 1.48) also. Subtract both values.

P(z < 1.48) = 0.931

P(z < 1.26) = 0.896

Subtract the values above: 0.931 - 0.896 = 0.035. Thus:

P(1.26 < z < 1.48) = 0.035

b) Find c such that: P(z < c) = 0.1288

We need to use the inverse Normal Distribution, enter the probability and find the z-score: c = -1.132