8.| Insurance: Claims Do you try to pad an insurance claim to cover your de- duc

Question

8.| Insurance: Claims Do you try to pad an insurance claim to cover your de- ductible? About 40% of all U.S. adults will try to pad their insurance claims! (Source: Are You Normal?, by Bernice Kanner, St. Martin's Press.) 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. What is the probability that (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?

Explanation / Answer

Solution:-

p = 0.40

a) The probability that half or more of the claims have been padded is 0.01384.

x = 64

By applying binomial distribution:-

P(x, n) = nCxpx*(1-p)(n-x)

P(x > 64) = 0.01384

b) The probability that fewer than 45 claims have been padded is 0.11274.

x = 45

By applying binomial distribution:-

P(x, n) = nCxpx*(1-p)(n-x)

P(x < 45) = 0.11274

c) The probability that from 40 to 64 of the claims have been padded is 0.9607.

x1 = 40

x2 = 64

By applying binomial distribution:-

P(x, n) = nCxpx*(1-p)(n-x)

P(40 < x < 64) = P(x > 40) - P(x > 64)

P(40 < x < 64) = 0.9745 - 0.013843

P(40 < x < 64) = 0.9607

d)  The probability that more than 80 of the claims have not been padded is 0.2534.

p = 0.60

x = 80

By applying binomial distribution:-

P(x, n) = nCxpx*(1-p)(n-x)

P(x > 80) = 0.2534

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