Determine whether the distributions represent a probability distribution. If it does not, state why. Numbers 1 – 2.

1. X P(X)
1 1/10
2 3/10
3 1/10
4 2/10
5 3/10

2. X P(X)
5 .3
10 .4
15 .1

3. A large retail company encourages its employees to get customers to apply for the store credit card. Below is the distribution for the number of credit card applications received per employee for an 8-hour shift.

X P(X)
0 .27
1 .28
2 .20
3 .15
4 .08
5 .02

a. What is the probability that an employee will get 2 or 3 applications during any given shift?

b. Find the mean, variance, and standard deviation for this probability distribution.

4. A box contains 5 pennies, 3 dimes, 1 quarter, and 1 half dollar. A coin is drawn at random. Construct a probability distribution for this data.

5. If a 60-year-old buys a $5000 life insurance policy at a cost of $250 and has a probability of .85 of living to age 61, find the expectation of the policy.

6. A producer plans an outdoor regatta for May 3. The cost of the regatta is $8000. This includes advertising, security, printing tickets, entertainment, etc. The producer plans to make $15,000 profit if all goes well. However, if it rains, the regatta will have to be canceled. According to the weather report, the probability of rain is 0.3. Find the producer’s expected profit.

7. A game is set up as follows: All the diamonds are removed from a deck of cards, and these 13 cards are placed in a bag. The cards are mixed up, and then one card is chosen at random (and then replaced). The player wins according to the following rules.

If the ace is drawn, the player loses $20
If a face card is drawn, the player wins $10
If any other card (2-10) is drawn, the player wins $2.

How much should be charged to play this game in order for it to be fair?

8. Let X be a binomial random variable with n = 12 and p = .3. Find the following:
a. P(X=8)=

b. P(X<5)=

c. P(X≥10)=

d. P(4

9. In a retirement community, 14% of cell phone users use their cell phones to access the Internet. In a random sample of 10 cell phone users, what is the probability that exactly 2 have used their phones to access the Internet? More than 2?

10. If 80% of job applicants are able to pass a computer literacy test, find the mean, variance, and standard deviation of the number of people who pass the examination in a sample of 150 applicants.

11. The chance that a U. S. police chief believes the death penalty “significantly reduces the number of homicides” is 1 in 4. If a random sample of 8 police chiefs is selected, find the probability that at most 3 believe that the death penalty significantly reduces the number of homicides.

12. Three out of four American adults under age 35 have eaten pizza for breakfast. If a random sample of 20 adults under age 35 is selected, find the probability that exactly 16 have eaten pizza for breakfast.

13. Computer Help Hot Line receives, on average, 6 calls per hour asking for assistance. For any randomly selected hour, find the probability that the company will receive

a. At least 6 calls

b. 4 or more calls

c. At most 5 calls

d. What is the mean, variance and standard deviation?

14. The number of boating accidents on Lake Emilie follows a Poisson distribution. The probability of an accident on Lake Emilie is 0.003. If there are 1000 boats on the lake during a summer month, find the probability that there will be 6 accidents.

15. A coin is tossed 6 times. Find the probability of getting exactly 4 heads.

16. A coin is tossed 6 times. Find the mean, variance, and standard deviation for the number of heads that will be tossed.

17. Construct a valid probability distribution for the number of boys a couple could have if they were to have 4 children.

18. A nationwide survey of 1001 people by the University of Connecticut Center for Survey Research and Analysis found that 20% of men aged 18 to 29 had tattoos. (The Hartford Courant, October 22, 2002). Suppose that this result holds true for the current population of all men in this age group. Find the probability that in a random sample of 500 men aged 18 to 29, 80 to 110 have tattoos.

19. According to an estimate, 50% of the people in America have at least one credit. If a random sample of 30 persons is selected, what is the probability that less than 19 of them will have at least one credit card?

20. What value would be needed to complete the following probability distribution?

X P(X)
0 1/3
1 1/8
2 1/8
3 ___
4 1/6