A binomial experiment is given. Decide whether you can use the normal distributi

Question

A binomial experiment is given. Decide whether you can use the normal distribution to approximate the binomial distribution. If you? can, find the mean and standard deviation. If you? cannot, explain why.

A survey of adults found that

90?%

read every word or at least enough to understand a contract for buying or selling a home before signing. You ask

14

adults selected at random if he or she reads every word or at least enough to understand a contract for buying or selling a home before signing.

Select the correct answer below? and, if? necessary, fill in the answer boxes within your choice.

A.

The normal distribution cannot be used to approximate the binomial distribution because

nqless than<5.

B.

The normal distribution cannot be used to approximate the binomial distribution because

npless than<5.

C.

The normal distribution can be used to approximate the binomial distribution. The mean is

(blank)

and the standard deviation is

(blank).

?(Round to two decimal places as? needed.)

Explanation / Answer

Given,

n = 14, p = 0.90

q = 1 - p = 1 - 0.90 = 0.10

Hence,

np = 14(0.90) = 12.6

nq = 14(0.10) = 1.4

Hence,

The normal distribution cannot be used to approximate the binomial distribution because nq < 5.

Option A is correct.

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