# MATHEMATICS

- What is the age distribution of promotion-sensitive shoppers? A
*supermarket super shopper*is defined as a shopper for whom at least 70% of the items purchased were on sale or purchased with a coupon.Age range, years 18-28 29-39 40-50 51-61 62 and over Midpoint *x*23 34 45 56 67 Percent of super shoppers 5% 41% 26% 11% 17% For the 62-and-over group, use the midpoint 67 years.

(a) Using the age midpoints*x*and the percentage of super shoppers, do we have a valid probability distribution? Explain.(b) Use a histogram to graph the probability distribution of part (a).

(c) Compute the expected age

*μ*of a super shopper. (Round your answer to two decimal places.)

*μ*=(b) Use a histogram to graph the probability distribution in part (a).

(c) Find the probability that a British nurse selected at random in 1851 would be 60 years of age or older. (Round your answer to three decimal places.)

(b) Find the probability that two or more of the five parolees will be repeat offenders. (Round your answer to three decimal places.)

How much did Kevin effectively contriute to the Samaritan Center for the Homeless? (Round your answer to two decimal places.)

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- Sara is a 60-year-old Anglo female in reasonably good health. She wants to take out a $50,000 term (that is, straight death benefit) life insurance policy until she is 65. The policy will expire on her 65th birthday. The probability of death in a given year is provided by the Vital Statistics Section of the
*Statistical Abstract of the United States*(116th Edition).*x*= age60 61 62 63 64 *P*(death at this age)0.00634 0.00809 0.00875 0.00972 0.01126 Sara is applying to Big Rock Insurance Company for her term insurance policy.

(a) What is the probability that Sara will die in her 60th year? (Use 5 decimal places.)

[removed]Using this probability and the $50,000 death benefit, what is the expected cost to Big Rock Insurance?

$ [removed](b) Repeat part (a) for ages 61, 62, 63, and 64.

Age Expected Cost 61 $ [removed] 62 $ [removed] 63 $ [removed] 64 $ [removed] What would be the total expected cost to Big Rock Insurance over the years 60 through 64?

$ [removed](c) If Big Rock Insurance wants to make a profit of $700 above the expected total cost paid out for Sara’s death, how much should it charge for the policy?

$ [removed](d) If Big Rock Insurance Company charges $5000 for the policy, how much profit does the company expect to make?

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