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 64% are familiar with international humanitarian law. You randomly select 50 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. B. No, because nq

Explanation / Answer

no of adults selected i.e n = 50

proportion of adults who are familiar with International humanitarian law i.e p = 0.64

q = 1-p = 1-0.64 = 0.36

np = 50*0.64 = 32 > 5

nq = 50(0.36) = 18 > 5

so we can use normal distribution to approximate bionomial distribution as np>5 and nq>5

mean = np = 50*0.64 = 32

variance = np(1-p) = 50*0.64*(1-0.64) = 11.52

standard deviation = variance = 11.52 = 3.39

so answer is (a)Yes the mean is 32 and standard deviation is 3.39

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