1. The following frequency histogram shows the scores for seventeen students in a quiz.

a. (2 pts) Find the number of students who scored less than 60 on the quiz.

b. (2 pts) Find the percentage of students who scored 80 or higher.

c. (5 pts) Find the approximate mean.

2. Given the following set of data of nine night temperatures

-2, 0, 0, 4, -2, 1, 6, -1, 0

a. (6 pts) Find Q1, Q2 and Q3.

b. (1 pts) Find the interquartile range (IQR)

c. (3 pts) Draw a box-plot and comment on the shape of the distribution.

3. Consider the following two variables X and Y:

X

1

1

4

15

Y

8

9

5

0

a. (2 pts) Find the mean of X, and mean of Y

b. (2 pts) Find the standard deviation of X, and standard deviation of Y

c. (4 pts) Find the covariance between X and Y.

d. (2 pts) Find correlation between X and Y and comment on your answer.

4. Male and Female students at a high school were surveyed about their career preferences. The data are shown in the table below.

Doctor

Engineer

Other

Male

10

12

25

Female

15

8

27

a. (2 pts) What is the probability that a randomly selected student wants to be an Engineer?

b. (2 pts) What is the probability that a randomly selected student is a Female and wants to be a Doctor?

c. (3 pts) What is the probability that a randomly selected student wants to be a Doctor, given that the student is Male?

d. (3 pts) What is the probability that a randomly selected student is Male, given that this student wants to be Doctor?

5. The random variable Y can take values -1, 0, 1 and 2 only. The probability distribution of Y is given below.

Y

P(Y)

-1

0.05

0

0.30

1

0.20

2

c

a. (2 pts) Find the value of c.

b. (2 pts) What is the probability that Y is less than or equal to 1? (i.e. ) )

c. (2 pts) Find the expected value of Y.

6.

a. (3 pts) A team is being formed that includes 11 different people. There are different positions on the team. How many different ways are there to assign the 11 people to the 11 positions?

b. (3 pts) A student has 9 course books that she would like to place in her backpack. However, she only has room for 3 books. Regardless of the arrangement, how many ways are there she can select 3 books into her backpack?

7. In a hospital, 40% of the patients are male. 12% of the male patients have disease X, and 20% of the female patients do not have disease X.

a. (2 pts) If a patient is selected at random, what is the probability that the patient has disease X?

b. (2 pts) If a patient is selected at random, what is the probability that the patient is a female and have disease X?

c. (2 pts) Given that a randomly selected patient does not have disease X, what is the probability that the patient is male?

8. Suppose that you and two friends go to a restaurant, which last month completed approximately 85% of orders correctly. Assume a binomial distribution.

a. (3 pts) What is the probability that all 3 orders will be completed correctly?

b. (3 pts) What is the probability that at least one order is completed correctly?

c. (2 pts) What is the expected number of correctly completed orders?

9. Assume that the number of network errors experienced in a day on a Local Area Network (LAN) is distributed as a Poisson random variable. The mean number of network errors experienced is 1.7 per day.

a. (3 pts) What is the probability that on a given day there are no errors?

b. (3 pts) What is the probability that on a given day there are 1 or 2 errors?

c. (3 pts) What is the probability that there are exactly 5 errors in 2 days?

10. The annual ground coffee expenditures for households are approximately normally distributed, with a mean of $49 and a standard deviation of $13.

a. (3 pts) Find the probability that a household spent less than $25.

b. (3 pts) Find the probability that a household spent more than $50.

c. (2 pts) What proportion of the households spent between $22 and $30?

d. (2 pts) 98.5?% of the households spent less than what? amount?

11. A study of the time spent shopping in a supermarket for specific items showed an approximately uniform distribution between 20 minutes and 45 minutes.

a. (2 pts) Write the probability density function and graph it.

b. (2 pts) What is the probability that the shopping time will be between 32 and 38 minutes?

c. (4 pts) What are the mean and standard deviation of the shopping time?

12. The weights of newborn babies are normally distributed with a mean of 3.05 kg and a standard deviation of 0.45 kg. A random sample of 25 newborn babies is selected.

a. (2 pts) What is the standard error for the sample mean?

b. (6 pts) What is the probability that the sample mean weight of babies is less than 2.80 kg?