**Chapter 5 Review Sheet:**
1) A TV sports commentator claims that 45% of all football injuries are knee injuries. Assuming that this claim is true, what is the probability that in a game with five reported injuries
a) all are knee injuries?
b) none are knee injuries?
c) at least three are knee injuries?
d) no more than two are knee injuries?
2) In Summit County 65% of the voter population are Republicans. What is the probability that a random sample of ten Summit County voters will contain
a) exactly eight Republicans?
b) exactly two Republicans?
3) Only three out of four patients who have are artery bypass heart operation are known to survive five years without needing another bypass operation. Of seven patients who recently had such an operation, what is the probability that
a) all will survive five years without needing another operation?
b) at least four will survive five years without needing another operation?
c) exactly four will survive five years without needing another operation?
4) Long-term history has shown that 65% of all elected offices in the Gunnison County, Colorado have been won by Republican candidates. This year there are 5 public offices up for election. Use the above estimate for the probability of a Republican being elected to office and let r be the number of public offices won by Republicans.
a) Find P(r) for r = 0, 1, 2, 3, 4, 5.
b) Make a histogram for the r probability distribution.
c) What is the expected number of Republicans who will win office in the coming election?
d) What is the standard deviation of the r distribution?
e) Find the probability that three or more Republicans will win office.
f) Find the probability that two or fewer Republicans will win office.
5) Jim is an automobile salesman at Courtesy Cars, Inc. He has a history of making a sale for about 15% of all the customers to whom he shows automobiles and goes out on test drives with eight customers. Use the above estimate for the probability of a single sale and let r be the number of sales on a day when Jim has eight customers.
a) Find P (r) for r = 0, 1, 2, 3, 4, 5, 6, 7, 8.
b) Make a histogram for the r probability distribution.
c) What is the expected number of cars Jim will sell if he has eight customers?
d) What is the standard deviation of the r distribution?
e) What is the probability that Jim will sell at least one car on a day when he has eight customers?
f) What is the probability that Jim will sell two or fewer cars on a day when he has eight customers?
6) Evaluate the following when n = 10 and p = .72
a) Probability when r = 6 _______________
b) Probability when r is at most 7 _______________
c) Probability when r is at least 6 _______________
d) Probability when r __>__ 6 _______________
e) Probability when r < 10 _______________
7) An agricultural school claims to have invented a hormone that will cause 85% of the laying hens receiving the hormone to produce some eggs each day. The hormone was given to a random sample of 500 hens one day on Zent’s farm.
a) Find the probability that 422 of the hens will lay some eggs each day.
________________
b) Find the probability that 0 hens will lay some eggs each day.
________________
8) Suppose the average number of phone calls received by a business is 4 in a 13 minute period.
a) Find the probability that no calls will be received in a 13 minute period.
_______________
b) Find the probability that 5 calls will be received in a 26 minute period.
_______________
c) Find the probability that 3 calls will be received in a 6.5 minute period.
_______________
d) Find the probability that 10 calls will be received in a one hour and five minute period. _______________
9) The probability that a new medication produces a bad side effect is 0.02.
a) Find the probability that the first person with a bad side affect will appear on the 10^{th} person. _______________
b) Find the probability that the first person with a bad side effect will appear before the 3^{rd} person selected. _______________
c) Find the probability that the first person with a bad side effect will be exactly the 14^{th} person selected. ________________
10) A fair coin is flipped 10 times.
a) Find the probability of getting 5 heads. ________________
b) Find the probability of at least 4 tails. ________________
c) Find the probability of more than 6 heads. ________________
d) Find the probability of at or above 3 tails. ________________
11) A biologist has found that 40% of all brown bears are infected with trichinosis.
a) Find the probability that the third bear selected will have trichinosis.
________________
b) Find the probability that the 6^{th} bear selected will have trichinosis.
________________
c) Find the probability that the first bear with trichinosis will appear after the 3^{rd} bear selected. ________________
d) Find the probability that the first bear with trichinosis will appear after before the 5^{th} bear selected. ________________
12) Suppose the average number of people entering a bank in a 30 minute period is 8.
a) Find the probability that exactly 10 people will enter the bank in the next 30 minutes? _______________
b) Find the probability that 10 customers will come into the bank in the next hour? _______________
c) Find the probability that 12 customers will come into the bank in the next 1.5 hour period. _______________
**Share with your friends:** |