3. Theif! There are 12 batteries on Mrs. Garcia’s desk, unknowing to you 4 of the batteries are dead. You steal a random sample of 2 batteries for your calculator.a. Create a tree diagram representing the situation described.b. Create a probability model for the number of good batteries you get.c. What’s the expected number of good ones you have stolen?d. What’s the standard deviation?

4. Insurance companies use statistics to analyze how much money policy holders should pay in order to payout on claims made while maintaining a profit for the owners. For simplicity:Insurance Company StayAlive insures 10,000 women (all approximately the same age, good health, etc) for a policy worth a payout of $100,000 if policyholder dies or $50,000 if permanently disabled. Based on the insurance company’s analysis, they expect only one woman to pass away and two to become permanently disabled out of the 10,000 policy holders.a. What is the insurance company’s expected payout?b. What is the variance of payout in this situation?c. What is the expected payout and standard deviation if the company doubles the payout for anyone of the 10,000 women policyholders?d. Assuming each policy is independent, what would be the total expected payout and standard deviation for any two of the women policyholders?
5. On your drive (or ride) to school you have to pass through a total of 3 traffic lights. Assuming you stop when the light is red, the probability model of the number of stops needed and likelihood of number of red lights is shown in the table.a. How many red lights should you expect to “hit” each day?b. What’s the standard deviation?Assuming each day is independent: c. What is the expected number of red lights to hit on your way to school during a 5-day school week?d. What is the standard deviation for this five-day time span?
R=# of red lights
0
1
2
3
P(R = r)
.05
.20
.30
.45
Policyholder
outcome
Payout, Y
Probability
P(Y = y)
Death
$100,000
10000
1
Disabled
$50,000
10000
2
Neither
$0
10000
9997

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- Summer '16
- Calculus