Question

1.The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.5 minutes and a standard deviation of 3.1 minutes. Assume that the distribution of taxi and takeoff times is approximately normal. You may assume that the jets are lined up on a runway so that one taxies and takes off immediately after the other, and that they take off one at a time on a given runway.

(a) What is the probability that for 33 jets on a given runway, total taxi and takeoff time will be less than 320 minutes? (Round your answer to four decimal places.)

(b) What is the probability that for 33 jets on a given runway, total taxi and takeoff time will be more than 275 minutes? (Round your answer to four decimal places.)

(c) What is the probability that for 33 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes? (Round your answer to four decimal places.)

2.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 120 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 probability that for 33 jets, total taxi and takeoff time will be less than 320 minutes is,

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(b) The probability that for 33 jets, total taxi and takeoff time will be more than 275 minutes is,

ans.

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(c)

ans.

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Given:

Sample size n = 120

Probability of success p = 0.38

Probability of failure q = 1 - p = 1 -0.38 = 0.62

Thus, np = (120)(0.38) = 45.6, nq = (120)*(0.62) = 74.4

Thus, condition np > 5 and nq > 5 is satisfied

Mean:

Standard deviation:

(a) half or more of the claims have been padded

Now using probability correction:

ans,

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(b)  fewer than 45 of the claims have been padded

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(c) from 40 to 64 of the claims have been padded

ans.

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(d) more than 80 of the claims have not been padded

ans.