# The probability distribution for the random variable x follows. x f ( x ) 20 .20 25 .15 30 .25 35 .40 a. Is this probability distribution valid? Explain. b. What is the probability that x = 30? c. What is the probability that x is less than or equal to 25? d. What is the probability that x is greater than 30?

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

#### Solutions

Chapter
Section
Chapter 5.2, Problem 7E
Textbook Problem
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## The probability distribution for the random variable x follows. x f (x) 20 .20 25 .15 30 .25 35 .40 a. Is this probability distribution valid? Explain. b. What is the probability that x = 30? c. What is the probability that x is less than or equal to 25? d. What is the probability that x is greater than 30?

Expert Solution

a.

To determine

Check whether the probability distribution is valid or not.

### Explanation of Solution

Calculation:

The probability distribution of the random variable x is as follows:

 x f(x) 20 0.20 25 0.15 30 0.25 35 0.40

The rules for a discrete probability distribution are,

• The sum of the probabilities must equal to 1. That is, f(x)=1
• Each probability must be between 0 and 1, inclusive. That is, 0f(x)1

The random variable x takes values x=20,25,30,35

Expert Solution

b.

To determine

Find the probability at x=30.

Expert Solution

c.

To determine

Find the probability that x is less than or equal to 25.

Expert Solution

d.

To determine

Find the probability that x is greater than 30.

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