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1

Consider a binomial experiment with20trials and probability0.55of success on a single trial.(a) Use the binomial distribution to find the probability of exactly 10 successes. (Round your answer to three decimal places.) (b) Use the normal distribution to approximate the probability of exactly 10 successes. (Round your answer to four decimal places.) (c) Compare the results of parts (a) and (b).

These results are fairly different.These results are almost exactly the same.

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? About35%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 received120insurance 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

3

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. It is estimated that3.5%of the general population will live past their 90th birthday. In a graduating class of758high school seniors, find the following probabilities. (Round your answers to four decimal places.)(a) 15 or more will live beyond their 90th birthday (b) 30 or more will live beyond their 90th birthday (c) between 25 and 35 will live beyond their 90th birthday (d) more than 40 will live beyond their 90th birthday

4

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. Ocean fishing for billfish is very popular in the Cozumel region of Mexico. In the Cozumel region about41%of strikes (while trolling) resulted in a catch. Suppose that on a given day a fleet of fishing boats got a total of22strikes. Find the following probabilities. (Round your answers to four decimal places.)(a) 12 or fewer fish were caught (b) 5 or more fish were caught (c) between 5 and 12 fish were caught

5

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. It is known that76%of all new products introduced in grocery stores fail (are taken off the market) within 2 years. If a grocery store chain introduces61new products, find the following probabilities. (Round your answers to four decimal places.)(a) within 2 years 47 or more fail (b) within 2 years 58 or fewer fail (c) within 2 years 15 or more succeed (d) within 2 years fewer than 10 succeed