Question

in the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities.

Do you try to pad an insurance claum to cover your deductible? About 39% of all U.S. adults will try to pad their insurance claims! suppose that you are the director of an insurance adjustment office. Your office has just recieved 132 insurance claims to be processed in the next few days. find the following probabilities (round to four decimal places). (a) half or more of the claims have been padded (b) fewer than 45 of the claims have been padded (c) from 40 to 64 of the claims have been padded (d) more tban 80 of the claims have not been padded

Answer 1

Here,

P(a random insurance claim is padded)= p =0.39

n= 132,q=1-p= 0.61

Since, np =132*0.39 = 51.48

And n(1-p) = 132*0.61 = 80.52

Both of which are greater than 5 as needed.

Hence, normal approximation can be used here.

Mean = np = 51.48

Std dev = sqrt(npq) = 5.60382