   # Given that z is a standard normal random variable, compute the following probabilities. a. P (0 ≤ z ≤ 83) b. P (−1.57 ≤ z ≤ 0) c. P ( z &gt; .44) d. P ( z ≥ −.23) e. P ( z &lt; 1.20) f. P ( z ≤ −.71) 13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

#### Solutions

Chapter
Section 13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884
Chapter 6.2, Problem 12E
Textbook Problem
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## Given that z is a standard normal random variable, compute the following probabilities. a. P(0 ≤ z ≤ 83) b. P(−1.57 ≤ z ≤ 0) c. P(z > .44) d. P(z ≥ −.23) e. P(z < 1.20) f. P(z ≤ −.71)

a.

To determine

Compute the value of P(0z0.83).

### Explanation of Solution

Calculation:

The variable z follows a standard normal distribution.

The value of P(0z0.83) is,

P(0z0.83)=P(z0.83)P(z0)

From “Appendix B: Table 1 cumulative probabilities for the standard normal distribution”, the value of z under 0

b.

To determine

Compute the value of P(1.57z0).

c.

To determine

Compute the value of P(z0.44).

d.

To determine

Compute the value of P(z0.23).

e.

To determine

Compute the value of P(z<1.20).

f.

To determine

Compute the value of P(z0.71).

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