Question

Assume Z has a standard normal distribution. Use Appendix Table III to determine the value for z that solves each of the following:
(a) .

Enter your answer in accordance to the item a) of the question statement
(Round the answer to 2 decimal places.)

(b) .

Enter your answer in accordance to the item b) of the question statement
(Round the answer to 2 decimal places.)

(c) .

Enter your answer in accordance to the item c) of the question statement
(Round the answer to 2 decimal places.)

(d) .

Enter your answer in accordance to the item d) of the question statement
(Round the answer to 1 decimal place.)

Answer 1

The value of the z score form the normal distribution table will be 1.96, 2.58, 0.91, and 0.0014.

What is a normal distribution?

It should be noted that a normal distribution simply means a probability distribution which is symmetric about the mean.

From the complete question, value of the z score form the normal distribution table will be calculated thus:

P(-z < Z < z) = 0.95

1 - P(Z < - z) - P(Z > z) = 0.95

1 - P(Z > z) - P(Z > z) = 0.95

1 - 2 × P(Z > z) = 0.95

P(Z > z) = (1 - 0.95)/2 = 0.025

This will be 1.96 from the normal probability table.

For P(-z < Z < z) = 0.99

1 - P(Z < - z) - P(Z > z) = 0.99

1 - P(Z > z) - P(Z > z) = 0.99

1 - 2 × P(Z > z) = 0.99

P(Z > z) = (1 - 0.99)/2 = 0.005

This will be 2.58 from the normal probability table.

For P(-z < Z < z) = 0.64

1 - P(Z < - z) - P(Z > z) = 0.64

1 - P(Z > z) - P(Z > z) = 0.64

1 - 2 × P(Z > z) = 0.64

P(Z > z) = (1 - 0.64)/2 = 0.18

This will be 0.91 from the normal probability table.

For P(-z < Z < z) = 0.9973

1 - P(Z < - z) - P(Z > z) = 0.9973

1 - P(Z > z) - P(Z > z) = 0.9973

1 - 2 × P(Z > z) = 0.9973

P(Z > z) = (1 - 0.9973)/2 = 0.0014

This will be 2.99 from the normal probability table.

Therefore, the correct options are 1.96, 2.58, 0.91, and 0.0014.

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