STA200 Homework Based on Chapter 6. 1) Problem 8 page 249. For a fundraiser, 1000 raffle tickets are sold, and the winner is chosen at random. There is only one prize, $500, in cash. You buy one ticket. a) What is the probability you will win the prize of $5007 b) What are your expected earnings? c) If a ticket cost $2, what is the difference between your "costs" and "expected earnings"? How much are you effectively contributing to the fundraiser? Hint: The p(success) p=1/1000 p(failure) g=999/1000 Expected Value= 500*p +0*q 2) Problem page 251. Jim is a 60-year-old male in reasonably good health. He wants to take out a $50,000 term life insurance policy until he is 65. The policy will expire on his 5th birthday. The probability of death in a given year is this table: x=age --------- P(death at this age) Bl s i --0.01191 61 -mmmmmmmmmmemam e 0.01292 62 0.01396 B3 evrrmesemmmeresmsmmmm 0.01503 64 -mmmmmmmememeeee - (0.01613 Jim applied for his term insurance policy. a) What is the probability that Jim will die in his 60th year? What is the expected cost to the insurance company? b) Repeat for years 61,62,63, and 64. c) What would be the total expected cost to the insurance company over the years 60 through 647 Hint: for every age, p is given, g = 1 - p, and the expected value can be calculated. For example, for 62 years: p=0.01396, q=0.98604, expected value=0.01396*50,000 +0.98604*0=$698 3) Problem 15, page 266. A fair quarter is flipped three times. For each of the following probabilities, use the formula for the binomial distribution to compute the requested probability. a) Find the probability of getting exactly three heads. b) Find the probability of getting exactly two heads. c) Find the probability of getting two or more heads. d) Find the probability of getting exactly three trails. Hint: n=3, p=0.5, q=0.5, r is the expected heads for each case. Apply the formula of binomial probability for each value of r (0,1,2,3), or the Excel formula for each: =BINOM.DIST(n,r,p,FALSE) 4) Problem 12, page 276. The quality-control inspector of a production plant will reject a batch of syringes if two or more defective syringes are found in a sample of eight syringes taken from the batch. Suppose the batch contains 1% defective syringes. a) Make a histogram showing the probabilities of r=0,1,2,3,4,5,6,7, and 8 defective syringes in a random sample of eight syringes. Hint: calculate each probability where n=8, p=0.01, g=0.99, using =BINOM.DIST(n,r,p,FALSE) b) Find mu (pu)? What is the expected number of defective number of syringes the inspector will find? ) What is the probability that the batch will be accepted? Hint: apply the formula of expected value