Question 1

An insurance company will insure a $75,000 Hummer for its full value against theft at a premium of $1500 per year.Suppose that the probability that the Hummer will be stolen is 0.0075. Find the premium that the insurance company should charge if its wants it's expected net profit to be $2000?

Accepted Answer

2000 = (x-75000)(.0075)+ x (.9925)= .0075x - 562.5 + .9925x = 2562.5

Question 2

Suppose that x has a hypergeometric distribution with N = 10,r = 5 and n = 3.Calculate the standard deviation of the distribution.

Accepted Answer

n (r/N)(1 - r/N)((N-n)/(N-1))= 3 (5/10)(.5)(7/9)= .583 (variance)F1F1F1S1F1F1F10 .583 = .764 std dev

Question 3

An insurance company will insure a $75,000 Hummer for its full value against theft at a premium of $1500 per year.Suppose that the probability that the Hummer will be stolen is 0.0075. Calculate the insurance company's expected net profit.

Accepted Answer

= (-73500)(.0075)+ (1500)(.9925)= -551.25 + 1488.75 = 937.50

Question 4

A large disaster cleaning company estimates that 30% of the jobs it bids on are finished within the bid time.Looking at a random sample of 8 jobs that is has contracted: Calculate the mean number of jobs completed within the bid time.

Accepted Answer

= np = 8(.3)= 2.4

Question 5

A large disaster cleaning company estimates that 30% of the jobs it bids on are finished within the bid time.Looking at a random sample of 8 jobs that is has contracted: Find the probability that x (number of jobs finished on time)is within one standard deviation of the mean.

Accepted Answer

= 1.3,2.4 F1F1F1S1F1F1F10 1.3 = (1.1,3.7)- 2,3 (.2965)+ (.2541)= .5506

Question 6

A large disaster cleaning company estimates that 30% of the jobs it bids on are finished within the bid time.Looking at a random sample of 8 jobs that is has contracted: Calculate the probability that exactly 4 of the jobs were not completed within the bid time.

Accepted Answer

P(x = 4)= .1361

Question 7

If in a hypergeometric distribution r is 300,N = 600 and n = 150,estimate the binomial probability of success.

Accepted Answer

r/N = 300/600 = 0.500

Question 8

Suppose that x has a hypergeometric distribution with N = 10,r = 5 and n = 3.Calculate the mean of the distribution.

Accepted Answer

n (r/N)= 3 (5/10)= 1.5

Quiz 5: Discrete Random Variables