Question

3. Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a sketch to support your calculation.

a. If P( Z < a) = 0.9026, find a.

b. If P( Z > b) = 0.4656, find b.

c. If P( − d < z < d) )=0. 8740, find d .

Answer 1

Solution :

Using standard normal table,

a.

P(Z < a) = 0.9026

P(Z < 1.30) = 0.9026

a = 1.30

b.

P(Z > b) = 4656

1 - P(Z < b) = 0.4656

P(Z < b) = 1 - 0.4656

P(Z < 0.09) = 0.5344

b = 0.09

c.

P(-d Z d) = 0.8740

P(Z d) - P(Z -d) = 0.8740

2P(Z d) - 1 = 0.8740

2P(Z d) = 1 + 0.8740 = 1.8740

P(Z d) = 1.8740 / 2 = 0.937

P(Z 1.53) = 0.937

d = 1.53