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 claim to cover your deductible? About 36% 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 received 132 insurance claims to be processed in the next few days. Find the following probabilities. (Round your answers 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 than 80 of the claims have not been padded

Answer 1

a)

The following information has been provided about the population proportion and the sample size:

Population Proportion =	0.36
Sample Size =	132

We need to compute . Based on the information provided, the population men of sample proportions and the corresponding standard error are:

Observe that:

which indicates that the assumption for normal approximation for the sampling distribution is met.

Now, the following is obtained using normal approximation:

b) 45/132 = 0.34

We need to compute . Based on the information provided, the population men of sample proportions and the corresponding standard error are:

Now, the following is obtained using normal approximation:

c) 40/132 = 0.3

64/132 = 0.48

We need to compute . Based on the information provided, the population men of sample proportions and the corresponding standard error are:

Now, the following is obtained using normal approximation:

d)

80/132 = 0.61

We need to compute Based on the information provided, the population men of sample proportions and the corresponding standard error are:

Now, the following is obtained using normal approximation: