1.) An insurance company charges you $250 a year for an auto insurance policy. Assume the actual probability that you get in an accident during this year is .02 and that if you do get into an accident, the company will have to pay out $10,000 (i.e. they will receive $250 but lose $10,000 for a net loss of $9,750) and if you don't get into an accident the company gains the $250 you pay and loses nothing.

(a) What is the expected value to the company of this policy?

(b) What is the variance of the company's earnings from this policy?

(c) What is the standard deviation of the company's earnings from this policy?

2.) Using the normal probability tables in Appendix C.1 of the textbook, calculate each of the following: (For parts below that don't involve the standard normal, be sure to show your work, calculating a z-statistic first then looking up the probability)

(a) What is the probability a standard normal distribution gives a value less than 1.3?

(b) What is the probability a standard normal distribution gives a value less than -1.2?

(c) What is the probability a standard normal distribution gives a value greater than -2? 1

(d) What is the probability a normal distribution with = 3 and = 1 gives a value less than 4?

(e) What is the probability a normal distribution with = 2 and = 4 gives a value less than 4?

(f) What is the probability a normal distribution with = 100 and = 50 gives a value greater than 150?

3) Pretend that feelings toward Joe Biden in the American population follow a normal distribution with mean 46 and standard deviation 15.

(a) What is the probability that a randomly selected American will have feelings toward Biden above 70?

(b) What is the probability that a randomly selected American will have feelings toward Biden above 50?