In the following check that it is appropriate to use the normal appropriation to

Question

In the following check that it is appropriate to use the normal appropriation to the binomial. Then use the normal distribution its estimate the requested probabilities. Do you try to pad an insurance to cover your deductible? About 37% of all U.S adults will try to pad their insurance Islamic suppose that you are the director of an insurance adjustment office. Your office has just received 128 insurance claims to be processed in the next few days. Find the following probabilities. (a) half or more of the claims have been padded (b) fewer than 45 of the claims have beam padded (c) from 40 to 64 of the claims have been padded (d) more than SO of the claims have not been padded

Explanation / Answer

n= 128

p=0.37

mean = np = 0.37*128 = 47.36

standard deviation =np(1-p) = 128*0.63*0.37 = 29.8368

Using this mean and standard deviation for the normal distribution we calculate the requested probabilities:

a)P(X>64) = P(Z> (64-47.36)/29.8368) = P(Z>0.5577005577) = 0.2885

b)P(X<45) = P(Z<(45-47.36)/29.8368) =P(Z<-0.07909695409) = 0.5315

c)P(40<X<64) = P((40-47.36)/29.8368 < Z < (64-47.36)/29.8368) = P(-0.24667524667 < Z< 0.5577005577) = 0.3089

d)P(X<=80) =P(Z<(80-47.36)/29.8368 ) = 0.863

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