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 full-time workers found that 57% go to work when they are sick. You randomly select 35 full-time workers and ask them whether they go to work when they are sick. 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

p = 57% =0.57

q = 1-0.57= 0.43

n = 35

nq=35*0.43=15.05

np=35*0.57=19.05

as np and nq both greater than 5 normla distribution can be used

mean = np = nq=35*0.43=15.05

standard deviation = sqrt(npq)= sqrt(35*0.57*0.43)=2.928

so option a yes the mean is15.05 and the standard deviation is 2.92

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