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STAT 3000
Homework assignment 8
Due Wednesday, March 21, 2001
NAME: __________________________
Work on the homework individually or in groups (but everyone has to turn in his/her own assignment). Show your work as much as possible. You may use your calculator or software for all problems where it is not explicitly required to work by hand or with a software (in which case you will solve the problem as indicated). If you choose to use software, you do not have to provide the original printout – just copy the results from the screen. But remember: Answers copied from the back of your book do not bring you full credit!
Number of points you get for each problem is given in parentheses. You can get a maximum of 30 points for this homework.
I (6 pts) Binomial distribution
Please work on the following problems from Chapter 3, Section 3.1 of the Hayter book:
3.1.2 (2 pts - please solve 'by hand') 3.1.6 (2 pts), 3.1.7 (2 pts)
II (9 pts) Poisson distribution
Please work on the following problems from Chapter 3, Section 3.4 (and 'Supplementary problems') of the Hayter book:
3.4.2 (2 pts - please solve 'by hand'), 3.4.3 (2 pts), 3.4.4 (2 pts), 3.6.4 (3 pts)
Have a nice spring break!
III (15 pts) Review problems
1. (7 pts) Do all parts (a-g) of Problem 2.7.7 from the Hayter book (p. 157) 2. (3 pts) A life insurance company sells a term insurance policy to a 21-year old male that pays $100,000 if the insured dies within the next 5 years. The company collects a premium of $250 each year as payment for the insurance. The amount X that the company earns on this policy is $250 per year, less the $100,000 that it must pay if the insured dies. The table below shows the distribution of X :
Age at death Payout Probability 21 -$99,750 0. 22 -$99,500 0. 23 -$99,250 0. 24 -$99,000 0. 25 -$98,750 0. ≥ 26 $1250^?
a) Fill in the missing probability in the table and calculate the expected earnings Ε ( X ).
b) Under the terms given above, it would be quite risky for you as a life insurance agent to insure the life of only one 21-year-old person. There is a high probability that this person would live and you would gain $1,250 in premiums. But if this person were to die you would lose almost $100,000. Explain carefully why selling insurance is not risky for an insurance company that insures many thousands of 21-year-old men.
c) Calculate the variance Var ( X ) and the standard deviation σ x of the earnings.
3. (3 pts) Suppose that a grocery store purchases 5 cartons of skim milk at the wholesale price of $1.20 per carton and retails the milk at $1.65 per carton. After the expiration date, the unsold milk is removed from the shelf and the grocer receives a credit from the distributor equal to three-fourths of the wholesale price. If the probability distribution of the random variable X , the number of cartons that are sold from this lot, is given by
xi 0 1 2 3 4 5 pi (^) 151 152 152 153 154 153
Find the expected profit and the variance of the profit.
4. (2 pts) Do Problem 2.6.3 from the Hayter book (p. 155).
