A marketing manager at very big machines wants to ...



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STAT 211 SPRING 2002

You have 50 minutes to complete this exam. You can only use your own calculator and there is penalty of 5 pt. if you separate your exam with any reason.

There is no partial credit on this exam

If you did not mark your final answer on your scantron, your answer will be counted incorrect.

If you did not mark your exam form on the scantron or did not place it in the right folder at the end of the exam, your grade will not be changed.

If you caught cheating, you will get a grade of zero. Good Luck.

EXAM 2 - FORM A

Let X be a continuous random variable with the legitimate probability density function (pdf), [pic].

Answer questions 1 to 3 using this information.

1. Which of the following is the F(x) when 0 ( x ( 2 using the legitimate pdf?

a) 0

b) [pic]

c) [pic]

d) [pic]

e) 1

2. Which of the following is the 50th percentile of the random variable X using the legitimate pdf?

a) -4

b) -1.5874

c) -1.1547

d) 1.1547

e) 1.5874

3. Which of the following is the expected value of 2X using the legitimate pdf?

a) 3/8

b) 3/4

c) 1

d) 3/2

e) 3

Use the following choices to answer the next 3 questions.

(a) Binomial Distribution

(b) Hypergeometric Distribution

(c) Poisson distribution

(d) Exponential Distribution

(e) Geometric distribution

4. Suppose that 20% of the applicants to an engineering school are women. An admissions committee reviews applications in groups of 100. Which distribution would you use to find the probability that the number of women in the next group is greater than 25?

5. A computer time-sharing system receives teleport inquiries at an average rate of 0.1 per millisecond. Which distribution would you use to find the probability that the number of inquiries in a particular 50 millisecond stretch will be between 5 and 12?

6. A shipment contains 100 printed circuit boards. A sample of 10 boards will be tested. If 2 or fewer defectives are found, the shipment will be accepted. Assuming that 10% of the boards in the shipment are defective, Which distribution would you use to find the probability of accepting the shipment?

7. Find the value of c for P(Z ( c)=0.2236 where z is the standard normal random variable.

a) -0.58

b) -0.76

c) 0.58

d) 0.76

e) 1

8. Find the value of c for P(-c ( Z ( c)=0.5528 where z is the standard normal random variable.

a) -0.58

b) -0.76

c) 0.58

d) 0.76

e) 1

9. Find the value of c for P(|Z| ( c)=0.4472 where z is the standard normal random variable.

a) -0.58

b) -0.76

c) 0.58

d) 0.76

e) 1

When you toss a fair coin 4 times and count the number of tails (x), the legitimate probability distribution is

x 0 1 2 3 4

P(x) 1/16 1/4 6/16 1/4 1/16

Answer questions 10 to 12 using this information.

10. What is the probability that at least 2 tails are observed?

a) 2/16

b) 5/16

c) 11/16

d) 15/16

e) The probability distribution is not legitimate to compute it.

11. Which of the following is the expected number of tails?

a) 10/16

b) 1

c) 30/16

d) 95/64

e) 2

12. Which of the following is the variance of the number of tails?

a) 10/16

b) 1

c) 30/16

d) 95/64

e) 2

13. How would you determine if the given data come from a normal distribution?

a) I would graph data, x versus any f(x) to see if they make a symmetric graph.

b) I would graph data, x versus any f(x) to see if they make a 45( line.

c) I would graph the ordered data with their expected normality values to see if they make a symmetric graph.

d) I would graph the ordered data with their expected normality values to see if they make a 45( line.

e) I would graph data, x versus exponential f(x) to see if they make a 45( line.

14. Which of the following is the answer for [pic]?

a) 4

b) 5

c) 24

d) 120

e) 720

15. If time between failures are exponentially distributed with (=1, what is the median time between failures?

a) -0.50

b) -0.69

c) 0.69

d) 0.50

e) 1

16. If time between failures are exponentially distributed with (=1, what is the probability that the next failure occur in less than 5 minutes?

a) 0

b) 0.0067

c) 0.6321

d) 0.9933

e) 1

A joint pdf for x and y is defined by

[pic]

Answer questions 17 and 18 using this information.

17. Which of the following is the marginal pdf for X?

a) x+0.5 for all x

b) x, 0 ................
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