   # A random variable is normally distributed with a mean of m = 50 and a standard deviation of σ = 5. a. Sketch a normal curve for the probability density function. Label the horizontal axis with values of 35, 40, 45, 50, 55, 60, and 65. Figure 6.4 shows that the normal curve almost touches the horizontal axis at three standard deviations below and at three standard deviations above the mean (in this case at 35 and 65). b. What is the probability the random variable will assume a value between 45 and 55? c. what is the probability the random variable will assume a value between 40 and 60? 13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

#### Solutions

Chapter
Section 13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884
Chapter 6.2, Problem 9E
Textbook Problem
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## A random variable is normally distributed with a mean of m = 50 and a standard deviation of σ = 5. a. Sketch a normal curve for the probability density function. Label the horizontal axis with values of 35, 40, 45, 50, 55, 60, and 65. Figure 6.4 shows that the normal curve almost touches the horizontal axis at three standard deviations below and at three standard deviations above the mean (in this case at 35 and 65). b. What is the probability the random variable will assume a value between 45 and 55? c. what is the probability the random variable will assume a value between 40 and 60?

a.

To determine

Draw the normal curve for the probability density function.

### Explanation of Solution

Calculation:

The variable z is a normal variable with mean 50 and standard deviation 5.

Procedure:

Step-by-step procedure to draw the graph:

• Draw the horizontal axis and name it as x.
• Plot the points 35, 40, 45, 50, 55, 60, 65 along the x-axis...

b.

To determine

Find the probability that the normal variable z takes a value between 45 and 55.

c.

To determine

Find the probability that the normal variable z takes a value between 40 and 60.

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