   # Assume a binomial probability distribution has p = .60 and n = 200. a. What are the mean and standard deviation? b. Is this situation one in which binomial probabilities can be approximated by the normal probability distribution? Explain. c. What is the probability of 100 to 110 successes? d. What is the probability of 130 or more successes? e. What is the advantage of using the normal probability distribution to approximate the binomial probabilities? Use part (d) to explain the advantage. 13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

#### Solutions

Chapter
Section 13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884
Chapter 6.3, Problem 27E
Textbook Problem
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## Assume a binomial probability distribution has p = .60 and n = 200. a. What are the mean and standard deviation? b. Is this situation one in which binomial probabilities can be approximated by the normal probability distribution? Explain. c. What is the probability of 100 to 110 successes? d. What is the probability of 130 or more successes? e. What is the advantage of using the normal probability distribution to approximate the binomial probabilities? Use part (d) to explain the advantage.

a.

To determine

Find the mean and standard deviation.

### Explanation of Solution

Calculation:

The binomial probability distribution has p=0.60 and n=200.

The formula for mean in binomial distribution is,

μ=np

The formula for standard deviation is,

σ=np(1p)

The value of mean is,

μ=200×0.60=120

Thus, the mean is 120

b.

To determine

Explain whether the binomial distribution can be approximated to normal distribution or not.

c.

To determine

Find the probability of 100 to 110 successes.

d.

To determine

Find the probability of greater than or equal to 130 successes.

e.

To determine

Explain the advantage of using the normal distribution for approximation of binomial distribution.

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