BUSN5760 Midterm Examination

Answers must be clearly labeled, and work done-by-hand shown. Any partial credit given will be based upon work shown. Put your name on each page, and staple the pages together. Problems are worth 5 points each.

1. Let A be the set {-2, -2, -1,-1, 0, 1, 3, 3, 4, 4, 8, 8, 8, 9, 19}

a. Compute the mean of the numbers in set A

b. Compute the median of A.

c. Compute the mode of A.

d. Compute the variance of A.

e. Compute the standard deviation of A.

f. What number would have to be included in A to make its mean two?

h. What number would have to be included in A to triple its variance?

2. Alice, Bob, Chris, Don, Ed, Frank, Gary, Hank, Irene, Jack, Ken, Lane, Mary, Nancy, Olivia, Pete, Quinn, Ron, Steve, and Tony are candidates in an election to be corporate officers (President, Vice President, and Treasurer.)

How many outcomes can the election have?

How many outcomes can the election have that have Steve as President?

How many outcomes can the election have with either Alice or Ken as Vice President?

How many outcomes can the election have with neither Lane or Hank as Vice President?

3.) How many subsets does a set of 23 members have?

4.) Evaluate the following:

a. combinations of 10 things taken 6 at a time

b. permutations of 14 things taken 8 at a time

c. 0!

d. 10! + 9! + 8! – 7! – 6! – 5! – 4! – 3! – 2! – 1! – 0!

5.) John flips a fair, two-sided coin 8 times.

a. What is the probability that he flips exactly 4 heads?

b. What is the probability that he doesn’t get at least three heads?

c. What is the probability that he gets more heads than tails?

d. What is the probability that the fifth toss isn’t heads?

6.) If the probability of an outcome is r-to-s, what are the odds that the outcome will NOT occur?

7.) Among a group of 210 people, 150 either swim or jog, or both. 85 swim, and 60 both swim and jog.

a. How many jog?

b. How many neither swim nor jog?

8) You draw 1 card from a standard 52-card deck 5 times.

a. ?

b. What is the probability of getting exactly 3 red cards if the drawings are with replacement?

(9): Consider the two-stage experiment involving a six-sided die and three urns containing red, white, and blue chips.

The die has probabilities: p(1)=0.1, p(2)=0.1, p(3)=0.3, p(4)=0.2, p(5)=0.1

Urn I contains 2 red chips, 5 white chips, and 7 blue chips.

Urn II contains 1 red chip, 2 white chips, and 4 blue chips.

Urn III contains 5 red chips, 3 white chips, and 4 blue chips.

Stage 1: Roll the die, and counts the spots showing.

Stage 2: For 1 spot showing, draw a chip from Urn I and note its color

For 2 or 3 spots showing, draw a chip from Urn II and note its color

For 4, 5, or 6 spots showing, draw a chip from Urn III and note its color

Compute the following probabilities:

a. the chip selected is NOT blue

b. the chip selected is white, given that the die roll was 4

c. the die roll was 4, given that the chip selected was red

(10): You roll ten 6-sideddice. Each die has probability 1/3 of producing an odd number on a roll.

If you roll all ten dice, what is the probability that their sum is an odd number?

(11-12): Given the following jointly-ordered populations:

X ={ 2, 3, 5, 6, 9)

Y={10, 9, 8, 2, 1}

11. Find Cov(X,Y), Cov(Y,X), Cov(X,X)

12. Find Cov(Y,Y), rho(X,X), and rho(X,Y)

13.) Suppose that P(E)=0.6, P(F)=0.4, and P(E and F)=0.3. What is P(E or F)?

14.) Suppose that events E and F are independent. In addition, P(E)=0.4 and P(F)=0.3. What is P(E and F)?

15.) Suppose that P(E) = 0.6 and P(F|E) = 0.4. What is P(E and F)?

16.) Given the values n=21, p=0.6, and m=12, compute the probability of m successes in n independent trials of a binary experiment.

17.) Determine the area under the standard normal curve that lies to the left of z = -1.52

18.) Find the area under the standard normal curve that is either left of z = -1.74 or right of z = 1.74 (that is, the two-tailed area).

19.) Suppose a random sample of size n=49 is obtained from a population with

m=66 ands =19. What is the probability that the sample mean is less than or equal to 61.6?

20.) Find the area under the standard normal curve between Z= -1.25 and Z= 1.85.