Problem 8

An insurance company issues a policy on a car under the following conditions:

(i) The replacement cost of $45,000 will be paid for a total loss.

(ii) If it is not a total loss, but the damage is more than $19,000, then only $ 11,000 will be paid.

(iii) If the damage is costing $19,000 or less, then only $ 9,000 will be paid.

(iv) Nothing will be paid out if there is no damage.

Based on their internal research, the company estimates the probability of the first three events are 0.05, 0.15, and 0.25, respectively.

a) Compute the expected amount paid out in a year.

b) If the company wishes to make a profit of $250 a policy, what is the amount the company should charge per month?

Problem 9

A company that manufactures bicycles receives steel rods in large shipments from a supplier. From past experience, the manager knows that the lengths are approximately normally distributed. He takes a random sample of 14 rods. The lengths of the sampled rods are as follows:

12.75

12.12

11.90

11.94

12.05

11.97

12.01

12.08

13.05

12.12

12.14

12.12

12.14

13.28

The company needs rods with a length of 12 inches in order to assemble the bikes properly. Because too-large and too-small rods are unsuitable, shipments not meeting the requirement are sent back to the supplier. Help this manager determine whether the shipment should be accepted or rejected. Perform hypothesis testing.

Problem 10

In a study of heart surgery, one issue was the effect of drugs called beta-blockers on the pulse rate of patients during surgery. The available subjects were divided at random into two groups of 40 patients each. One group received a beta-blocker; the other group received a placebo. The pulse rate of each patient at a critical point during the operation was recorded. The treatment group had a mean pulse rate of 58 and a standard deviation of 10. For the control group, the mean pulse rate was 65 and the standard deviation was 5.Perform hypothesis testing.