Question 1197940: 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 38% 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 136 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 by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website! Binomial Distribution:
n = 136, p = .38
136*.38 and 136*.62 are > 5
Using the normal approximation and continuity correction factor.
(the continuity correction factor used as a Binomial Distribution is not continuous)
mean =136*.38= 51.68
sd =  = 5.66
Using TI or similarly an inexpensive calculator like an Casio fx-115 ES plus
P(x ≥ 68 ) = normpdf(67.5,9999, 51.68, 5.66)= .0026
P(x < 45 ) = normpdf(-9999, 44.5, 51.68, 5.66)= .1023
P( 40 ≤ x ≤ 64) = normcdf( 39.5,64.5, 51.68, 5.66) = .9725
P(x > 80) = normpdf(80.5,9999, 51.68, 5.66) = .0000002
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