**BUS 500 **

**Fundamental of Statistics**

** **

**Exam 1**

Due on Monday November 21, 2015

** **

**INSTRUCTIONS**

** **

(i) This is an open-book exam. A double-sided cheat sheet can be used.

(ii) The exam has a total of 40 points.

(iii) You must show all relevant work to receive credit.

(iv) A pocket calculator can be used. A laptop computer cannot be used.

(v) In answering a given part of a question, you may assume know the results of previous parts (even if you did not answer them).

(vi) The duration of the exam is 120 minutes.

HONOR CODE

In taking this exam, I acknowledge and accept the STU Honor code.

NAME (signed) **_______________________________________________**

NAME (printed) **_______________________________________________**

**All work must be shown** (in Microsoft Word) in order to receive credit for the quiz. (**Even if some problems are multiple choices, you still need to show ****all relevant work to receive credit**).

1. For which set of data will the mean, the median and the mode all be equal? (5 points)

a. 1,2,5,5,7

b. 1,1,1,2,5

c. 1,2,5,5,8,9

d. 1,1,1,2

2. a) What is the value of the sample standard deviation of the following set of scores?

-3, -2, -1, 0, 0, 1, 2, 3 (2 points)

b) What is the value of the estimated population standard deviation of the following set of scores? 11, 17, 1, 16, 12, 20 (2 points)

3. If the mean value of the weight of a particular brand of dog food bag is 20.6 pounds and standard deviation is 1.3, assume a normal distribution and calculate the amount of product produced that falls below the lower specification value of 19.7. (3 points)

4. X is a normally distributed variable with mean ** μ = 30** and standard deviation

**σ = 4**. Find

a) P(x < 40) (3 points)

b) P(x > 21) (3 points)

c) P(30 < x < 35) (4 points)

5. A survey of 34 students at the Wall College of Business showed the following majors:

Accounting 10

Finance 5

Info. Systems 3

Management 6

Marketing 10

Suppose you select a student and observe his or her major.

a. What is the probability he or she is a marketing major? (2 points)

b. What is the probability he or she is a finance major? (2 points)

6. a) Let P(X) = 0.55 and P(Y) = 0.35. Assume the probability that they both occur is 0.20. What is the probability of either X or Y occurring? (3 points)

b) Suppose Let P(A) = 0.40 and P(B|A) = 0.30. What is the joint probability of A and B? (3 points)

**BUS 500**

**Fundamental of Statistics**

** **

**Exam 1**

Due on Monday November 21, 2015

** **

**INSTRUCTIONS**

** **

(i) This is an open-book exam. A double-sided cheat sheet can be used.

(ii) The exam has a total of 40 points.

(iii) You must show all relevant work to receive credit.

(iv) A pocket calculator can be used. A laptop computer cannot be used.

(v) In answering a given part of a question, you may assume know the results of previous parts (even if you did not answer them).

(vi) The duration of the exam is 120 minutes.

HONOR CODE

In taking this exam, I acknowledge and accept the STU Honor code.

NAME (signed) **_______________________________________________**

NAME (printed) **_______________________________________________**

**All work must be shown** (in Microsoft Word) in order to receive credit for the quiz. (**Even if some problems are multiple choices, you still need to show ****all relevant work to receive credit**).

1. For which set of data will the mean, the median and the mode all be equal? (5 points)

a. 1,2,5,5,7

b. 1,1,1,2,5

c. 1,2,5,5,8,9

d. 1,1,1,2

2. a) What is the value of the sample standard deviation of the following set of scores?

-3, -2, -1, 0, 0, 1, 2, 3 (2 points)

b) What is the value of the estimated population standard deviation of the following set of scores? 11, 17, 1, 16, 12, 20 (2 points)

3. If the mean value of the weight of a particular brand of dog food bag is 20.6 pounds and standard deviation is 1.3, assume a normal distribution and calculate the amount of product produced that falls below the lower specification value of 19.7. (3 points)

4. X is a normally distributed variable with mean ** μ = 30** and standard deviation

**σ = 4**. Find

a) P(x < 40) (3 points)

b) P(x > 21) (3 points)

c) P(30 < x < 35) (4 points)

5. A survey of 34 students at the Wall College of Business showed the following majors:

Accounting 10

Finance 5

Info. Systems 3

Management 6

Marketing 10

Suppose you select a student and observe his or her major.

a. What is the probability he or she is a marketing major? (2 points)

b. What is the probability he or she is a finance major? (2 points)

6. a) Let P(X) = 0.55 and P(Y) = 0.35. Assume the probability that they both occur is 0.20. What is the probability of either X or Y occurring? (3 points)

b) Suppose Let P(A) = 0.40 and P(B|A) = 0.30. What is the joint probability of A and B? (3 points)

7. A uniform distribution is defined over the interval from 6 to 10,

a) What are the values for a and b? (1 point)

b) What is the mean of this uniform distribution? (1 point)

c) Find the probability of a value more than 7. (Round your answer to 2 decimal places.) (2 points)

d) Find the probability of a value between 7 and 9. (Round your answer to 1 decimal place.) (2 points)

7. A uniform distribution is defined over the interval from 6 to 10,

a) What are the values for a and b? (1 point)

b) What is the mean of this uniform distribution? (1 point)

c) Find the probability of a value more than 7. (Round your answer to 2 decimal places.) (2 points)

d) Find the probability of a value between 7 and 9. (Round your answer to 1 decimal place.) (2 points)