1.An overnight express company must include five cities on its route. How many different routes are possible, assuming that it does notmatter in which order the cities are included in the routing?

Number of different routes

2.Solve the following:

a.

(40!) / (35!) =

b.

₇P₄ =

c.

₅C₂ =

3.If you ask three strangers on campus about their birthdays, what is the probability that

a. All were born on Wednesday? (Round the final answer to 4 decimal places.)

Probability

b. All were born on different days of the week? (Round the final answer to 4 decimal places.)

Probability

c. None was born on Saturday? (Round the final answer to 4 decimal places.)

Probability

4.A population consists of 15 items, 10 of which are acceptable. In a sample of four items, what is the probability that exactly three are acceptable? (Round the final answer to 4 decimal places.)

Probability

5.The speed with which utility companies can resolve problems is very important. The Georgetown Telephone Company (GTC), reports that it can resolve customer problems the same day they are reported in 70% of the cases. Suppose that the 15 cases reported today are representative of all complaints.

a-1. How many of the problems would you expect to be resolved today? (Round the final answer to 1 decimal place.)

Number of Problems

a-2. What is the standard deviation? (Round the final answer to 4 decimal places.)

Standard Deviation

b. What is the probability that 10 of the problems can be resolved today? (Round the final answer to 4 decimal places.)

Probability

c. What is the probability that 10 or 11 of the problems can be resolved today? (Round the final answer to 4 decimal places.)

Probability

d. What is the probability that more than 10 of the problems can be resolved today? (Round the final answer to 4 decimal places.)

Probability

6.Three tables listed below show random variables and their probabilities. However, only one of these is actually a probability distribution.

A

B

C

X

P(X)

X

P(X)

X

P(X)

5

0.3

5

0.1

5

0.5

10

0.3

10

0.2

10

0.3

15

0.2

15

0.3

15

0.2

20

0.4

20

0.4

20

0.4

a. Which of the above tables is a probability distribution?

b. Using the correct probability distribution, find the probability that x is: (Round the final answers to 1 decimal place.)

1.

Exactly 15 =

2.

No more than 10 =

3.

More than 5 =

c. Compute the mean, variance, and standard deviation of this distribution.

1.

Mean

2.

Variance ²

3.

Standard deviation

7.If you ask three strangers on campus about their birthdays, what is the probability that

a. All were born on Wednesday? (Round the final answer to 4 decimal places.)

Probability

b. All were born on different days of the week? (Round the final answer to 4 decimal places.)

Probability

c. None was born on Saturday? (Round the final answer to 4 decimal places.)

Probability

8.An overnight express company must include five cities on its route. How many different routes are possible, assuming that it does notmatter in which order the cities are included in the routing?

Number of different routes

9.Solve the following:

a.

(40!) / (35!) =

b.

₇P₄ =

c.

₅C₂ =