3. (15%) Complete the missing counts of the table and answer the following questions:

0

A

B

C

Total

D

20

35

35

?

105

E

34

?

30

0

95

Total

54

66

?

15

200

a) P (A OR C)?

b) P (D|B)?

c) Are events A and E independent?

4. (10%) A group of four women and six men must select a five-person committee.

1. Find the probability of getting a committee of three women and two men.
2. Find the probability of getting a committee of one woman and four men.

B. Distribution

1. 5. (10%) (Discrete Random Variable) Based on his experience, a librarian observed that the number of books checked out by a person visiting the library has the following probabilities. Find the expected value and its standard deviation number of books checked out by one person.

Numbers of Books

1

2

3

4

Probability

.15

.35

.40

.10

6. (10%) (Binomial) Consider a binomial probability distribution with parameters n = 10 and p = .3.

a) Compute the mean and the standard deviation of the distribution.

b) P(X = 1 or 8)?

7. (10%) (Binomial to Normal) According to the Gallup poll, 40% of Americans 18 year-old or older stated that they had read at least 6 books within the past year. You conduct a random sample of 200 Americans 18 year-old or older.

Approximate the probabilitythat between 70 and 90, inclusive, read at least 6 books within the past year.

8. (10%) (Normal) The Wechsler Intelligence Scale for Children is approximately normally distributed, with mean 85 and standard deviation 12.

What intelligence score will place a child in the 95th percentile?

9. (10%) (Sample proportion) A Gallup survey indicated that 72% of 18- to 29-year-olds would prefer to start their own business rather than work for someone else.A random sample of 50018- to 19-year-olds is obtained.

Would it be unusual if the sample resulted in 375 or more who would prefer to start their own business?