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 63% are familiar with international humanitarian law. You randomly select 40 adults and ask them whether they are familiar with international humanitarian law.

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

A. Yes, the mean is _____ and the standard deviation is ____ (Round to two decimal places as needed.)

B. No, because np<5.

C.No, because nq<5.

Explanation / Answer

n = 40

p = 0.63

q = 1 - p = 0.37

np = 40 * 0.63 = 25.2

nq = 40 * 0.37 = 14.8

Since, np and nq both are greater than 5, we can use normal approximation

mean = np = 40 * 0.63 = 25.2

standard deviation = sqrt(n * p * q)

                              = sqrt(40 * 0.63 * 0.37)

                              = 3.05

So, correct option is Option-A) Yes, the mean is __25.2___ and the standard deviation is __3.05__

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