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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.

**Calculation:**

The binomial probability distribution has

The formula for mean in binomial distribution is,

The formula for standard deviation is,

The value of mean is,

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.

STATISTICS F/BUSINESS+ECONOMICS-TEXT

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