Question

# Using the Standard Normal Table found in your textbook, find the z-scores such that: (a) The...

Using the Standard Normal Table found in your textbook, find the z-scores such that: (a) The area under the standard normal curve to its left is 0.5 z = (b) The area under the standard normal curve to its left is 0.9826 z = (c) The area under the standard normal curve to its right is 0.1423 z = (d) The area under the standard normal curve to its right is 0.9394

a)

We have to find a such that

P( Z < a) = 0.5

In Z table find z score such that probabiity is 0.5

We get Z- score = 0

[ That is P( Z < 0) = 0.5 ]

b)

P( Z < a) = 0.9826

In Z table, find z-score for the probability 0.9896

z-score = 2.111

c)

P( Z > a) = 0.1423

P( Z < a ) = 1 - 0.1423

P( Z < a) = 0.8577

In Z table , find z-score such that probability is 0.8577,

z-score = 1.07

d)

P( Z > a) = 0.9394

P( Z < (-a) ) = 0.9394

In z table, z-score for the probability 0.9394 is

z-score = 1.55

So z-score = -1.55 .