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 that 3.8% of the general population will live past their 90th birthday. In a graduating class of 712 high 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

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.

More than a decade ago, high levels of lead in the blood put 81% of children at risk. A concerted effort was made to remove lead from the environment. Now, suppose only 14% of children in the United States are at risk of high blood-lead levels.

(a) In a random sample of 190 children taken more than a decade ago, what is the probability that 50 or more had high blood-lead levels? (Round your answer to three decimal places.)

(b) In a random sample of 190 children taken now, what is the probability that 50 or more have high blood-lead levels? (Round your answer to three decimal places.)

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 41% 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.)

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

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 41% 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

Do you take the free samples offered in supermarkets? About 58% of all customers will take free samples. Furthermore, of those who take the free samples, about 39% will buy what they have sampled. Suppose you set up a counter in a supermarket offering free samples of a new product. The day you were offering free samples, 323 customers passed by your counter. (Round your answers to four decimal places.)

(c) What is the probability that a customer will take a free sample and buy the product? Hint: Use the multiplication rule for *dependent* events. Notice that we are given the conditional probability *P*(buy|sample) = 0.39, while *P*(sample) = 0.58.

Do you try to pad an insurance claim to cover your deductible? About 41% 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 138 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

Do you take the free samples offered in supermarkets? About 56% of all customers will take free samples. Furthermore, of those who take the free samples, about 37% will buy what they have sampled. Suppose you set up a counter in a supermarket offering free samples of a new product. The day you were offering free samples, 329 customers passed by your counter. (Round your answers to four decimal places.)

(a) What is the probability that more than 180 will take your free sample?

(d) What is the probability that between 60 and 80 customers will take the free sample *and *buy the product? *Hint:* Use the probability of success calculated in part (c).

Do you take the free samples offered in supermarkets? About 56% of all customers will take free samples. Furthermore, of those who take the free samples, about 37% will buy what they have sampled. Suppose you set up a counter in a supermarket offering free samples of a new product. The day you were offering free samples, 329 customers passed by your counter. (Round your answers to four decimal places.)

(a) What is the probability that more than 180 will take your free sample?

(b) What is the probability that fewer than 200 will take your free sample?

(c) What is the probability that a customer will take a free sample and buy the product? Hint: Use the multiplication rule for *dependent* events. Notice that we are given the conditional probability *P*(buy|sample) = 0.37, while *P*(sample) = 0.56.

(d) What is the probability that between 60 and 80 customers will take the free sample *and *buy the product? *Hint:* Use the probability of success calculated in part (c).

Do you take the free samples offered in supermarkets? About 58% of all customers will take free samples. Furthermore, of those who take the free samples, about 39% will buy what they have sampled. Suppose you set up a counter in a supermarket offering free samples of a new product. The day you were offering free samples, 323 customers passed by your counter. (Round your answers to four decimal places.)

(a) What is the probability that more than 180 will take your free sample?

(b) What is the probability that fewer than 200 will take your free sample?

(c) What is the probability that a customer will take a free sample and buy the product? Hint: Use the multiplication rule for *dependent* events. Notice that we are given the conditional probability *P*(buy|sample) = 0.39, while *P*(sample) = 0.58.

(d) What is the probability that between 60 and 80 customers will take the free sample *and *buy the product? *Hint:* Use the probability of success calculated in part (c).

(a) What is the probability that more than 180 will take your free sample?

(b) What is the probability that fewer than 200 will take your free sample?

(c) What is the probability that a customer will take a free sample and buy the product? Hint: Use the multiplication rule for *dependent* events. Notice that we are given the conditional probability *P*(buy|sample) = 0.39, while *P*(sample) = 0.58.

*and *buy the product? *Hint:* Use the probability of success calculated in part (c).

What’s your favorite ice cream flavor? For people who buy ice cream, the all-time favorite is still vanilla. About 21% of ice cream sales are vanilla. Chocolate accounts for only 11% of ice cream sales. Suppose that 180 customers go to a grocery store in Cheyenne, Wyoming, today to buy ice cream. (Round your answers to four decimal places.)

(a) What is the probability that 50 or more will buy vanilla?

(b) What is the probability that 12 or more will buy chocolate?

(c) A customer who buys ice cream is not limited to one container or one flavor. What is the probability that someone who is buying ice cream will buy chocolate or vanilla? *Hint*: Chocolate flavor and vanilla flavor are not mutually exclusive events. Assume that the choice to buy one flavor is independent of the choice to buy another flavor. Then use the multiplication rule for independent events, together with the addition rule for events that are not mutually exclusive, to compute the requested probability.

(d) What is the probability that between 50 and 60 customers will buy chocolate or vanilla ice cream? *Hint*: Use the probability of success computed in part (c).

What’s your favorite ice cream flavor? For people who buy ice cream, the all-time favorite is still vanilla. About 21% of ice cream sales are vanilla. Chocolate accounts for only 11% of ice cream sales. Suppose that 180 customers go to a grocery store in Cheyenne, Wyoming, today to buy ice cream. (Round your answers to four decimal places.)

(d) What is the probability that between 50 and 60 customers will buy chocolate or vanilla ice cream? *Hint*: Use the probability of success computed in part (c). The C is 0.2969

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