1. David’s gasoline station offers 16 cents off per gallon if the customer pays in cash and does not use a credit card. Past evidence indicates that 40% of all customers pay in cash. During a one-hour period, 15 customers buy gasoline at this station. What is the probability that at least 10 pay in cash?
0.024
0.033
0.009
0.976
2. For a binomial distribution, the mean is 0.6 and n = 2. What is p for this distribution?
0.5
1
0.3
0.1
x P(x)
0 0.900
1 0.090
2 0.007
3 0.003
3. For the probability distribution.
What is the standard deviation of the distribution?
2.1
1.14
0.364
0.564
4. The random variable Y tilde B i n open parentheses 3 comma space 0.2 close parentheses. The mean of the distribution is
1.5
0.6
0.25
0
x P(x)
0 0.9038
1 0.0880
2 0.0070
3 or more 0.0012
5. The following is a Poisson probability distribution with lambda equals 0.6
The variance of the distribution is _____.
1.5
0.6
0.75
1
6. The marketing department of a nationally known cereal maker plans to conduct a national survey to find out whether or not consumers of flake cereals can distinguish one of their favorite flake cereals. To test the questionnaire and procedure to be used, eight persons were asked to cooperate in an experiment. Five very small bowls of flake cereals were placed in front of a person. The bowls were labelled A, B, C, D, and E. The person was informed that only one bowl contained his or her favorite flake cereal. Suppose that the eight persons in the experiment were unable to identify their favorite cereal and just guessed which bowl it was in. What is the probability that none of the eight guessed correctly?
0.168
0.009
0.788
0.125
7. An insurance agent has appointments with four prospective clients tomorrow. From past experience, the agent knows that the probability of making a sale on any appointment is one out of five. What is the probability that the agent will sell a policy to three of the four prospective clients?
0.25
0.5
0.41
0.026
8. If the variance is 5.2 grams, what is the standard deviation?
2.2
2.8
22
27.04
9. Sweetwater & Associates write weekend trip insurance at a very nominal charge. Records show that the probability that a motorist will have an accident during the weekend and file a claim is 0.0005. Suppose they wrote 400 policies for the coming weekend, what is the probability that exactly two claims will be filed?
0.8187
0.25
0.0164
0.0001
10. In a large metropolitan area, past records revealed that 30% of all high school graduates go to college. From 20 graduates selected at random, what is the probability that exactly 8 will go to college?
0.114
0.887
0.4
0.231
11. A true/false test consists of six questions. If you guess the answer to each question, what is the probability of getting all six questions correct?
0
0.016
0.062
0.250
12. A farmer who grows genetically engineered corn is experiencing trouble with corn borers. A random check of 5,000 ears revealed the following: Many of the ears contained no borers. Some ears had one borer. A few had two borers, and so on. The distribution of the number of borers per ear approximated the Poisson distribution. The farmer counted 6,500 borers in the 5,000 ears. What is the probability that an ear of corn selected at random will contain no borers?
0.1235
0.2725
0.7759
0.1231
13. A new car was put into production. It involved many assembly tasks. Each car was inspected at the end of the assembly line and the number of defects per unit was recorded. For the first 100 cars produced, there were 40 defective cars. Some of the cars had no defects, a few had one defect, and so on. The distribution of defects followed a Poisson distribution. Based on the first 100 cars produced, about how many out of every 1,000 cars assembled should have one or more defects?
about 660
about 165
about 630
about 330
14. A manufacturer of headache medicine claims it is 70% effective within a few minutes. That is, out of every 100 users, 70 get relief within a few minutes. A group of 12 patients are given the medicine. If the claim is true, what is the probability that eight have relief within a few minutes?
0.001
0.168
0.667
0.231
15. The production department has installed a new spray machine to paint automobile doors. As is common with most spray guns, unsightly blemishes often appear because of improper mixtures or other problems. A worker counted the number of blemishes on each door. Most doors had no blemishes; a few had one; a very few had two; and so on. The average number was 0.5 per door.The distribution of blemishes followed the Poisson distribution. Out of 10,000 doors painted, about how many would have no blemishes?
about 6,065
about 3,935
about 5,000
about 500
16. A tennis match requires that a player win three of five sets to win the match. If a player wins the first two sets, what is the probability that the player wins the match, assuming that each player is equally likely to win each set?
0.5
0.125
0.875
0
17. A statistics professor receives an average of five e-mail messages per day from students. Assume the number of messages approximates a Poisson distribution. What is the probability that on a randomly selected day she will have five messages?
0.0067
0.875
0.1755
1
18. Sponsors of a local charity decided to attract wealthy patrons to its $500-a-plate dinner by allowing each patron to buy a set of 20 tickets for the gaming tables. The chance of winning a prize for each of the 20 plays is 50–50. If you bought 20 tickets, what is the chance of winning 15 or more prizes?
0.25
0.021
0.006
0.75
19. Judging from recent experience, 5% of the computer keyboards produced by an automatic, high-speed machine are defective. If six keyboards are randomly selected, what is the probability that none of the keyboards are defective?
0.001
0.167
0.735
0.5
x P(x)
1 0.05
2 0.30
3 0.40
4 0.25
20. The probability distribution shown below for the number of automobiles ( x) lined up at a Lakeside Olds dealer at opening time (7:30 AM) for service is
On a typical day, how many automobiles should Lakeside Olds expect to be lined up at opening time?
10
1
3
2
21. On a very hot summer day, 5% of the production employees at Midland States Steel are absent from work. The production employees are randomly selected for a special in-depth study on absenteeism. What is the probability of randomly selecting 10 production employees on a hot summer day and finding that none of them are absent?
0.002
0.344
0.599
0.1