In the following problem, check that it is appropriate to use the normal approxi

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 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 received 134 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

Explanation / Answer

Solution:-

p = 39/100

p = 0.39

n = 134

1)

a) The probability that half or more of the claims have been padded is 0.0063.

x = 67

By applying binomial distribution:-

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

P(x > 67) = 0.0063

b) The probability that fewer than 45 of the claims have been padded is 0.0836.

x = 45

By applying binomial distribution:-

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

P(x < 45) = 0.0836

c) The probability that from 40 to 64 of the claims have been padded is 0.9733.

x1 = 40

x2 = 64

By applying binomial distribution:-

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

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

P(40 < x < 64) = 0.9891 - 0.0158

P(40 < x < 64) = 0.9733

d) The probability that more than 80 of the claims have not been padded is 0.8235.

More than 80 of the claims have not been padded

That means 57 or fewer claims have been padded

x = 57

By applying binomial distribution:-

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

P(x < 57) = 0.8235

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