ENGR 6359 Test 1

Fall 1999     Instructor:  Dr. Ryan Underdown

 

Last  Name _______________________        First Name        ____________________

 

Student ID ______________________

 

Directions :  Answer all questions.  Show ALL WORK for full credit.

 

Show enough of your work to make it clear how you arrived on your answer.  Answers

without any work may lose credit if they are correct and will get no credit if incorrect. 

 

If you use Minitab, describe what you did in your answer. 

 

Each question has several parts; make sure you don’t miss any. Some questions may be more difficult than others for you; if you have trouble with a question, you may skip it and come back to it if you have time. If you need the answer to a previous part of a question to answer a later part of a question, but you were unable to answer that previous part, then describe what you would do if you had the answer to the previous part.

 

You may refer to your notes or books and use calculators.

1. The length of a drive shaft is made up of three parts, A, B, and C.  The lengths (in inches) of A, B, and C are statistically and normally distributed with the following means and variances.

 

 

m

s2

A

3

0.0025

B

4

0.0049

C

5

0.0036

 

What is the probability that the total length, Y=A+B+C, will exceed 12.2 inches? (20 points)

 

 

2. A sample of 50 physics test grades of a total of 200 yielded x = 65 and s = 10.

a)      What is a 95% confidence interval on the mean test score? (10 points)

b)      With what degree of confidence can we say that the mean score is 65+/- 1? (10 points)

 

 

3. A bottling machine is set so that it discharges a mean of 10 ounces per bottle.  The amount of fill dispensed by the machine is normally distributed with s = 1 ounce.  A sample of 16 filled bottles is taken from the output of the machine on a given day.  What is P(9.6 < X-bar < 10.4)? (20 points)

 

 

4. In early prototype production, the probability of a good unit is 0.65. How likely is it that a sample of 200 will provide between 110 and 135 good units? (20 points)

 

 

Choose either 5 or 6:

 

5. Out of the last 3960 random tests of a production process, 192 of the sampled items were flawed.

a)      What is the probability that at least the next 30 items will be produced without imperfections? (7 points)

b)      What is the probability that more than 80 will be produced before 2 flaws? (7 points)

c)      What is the probability that more than 120 will be produced before 3 flaws? (6 points)

 

 

6. Consider successive rolls of a fair die. Let rolling a 2 be considered a success and all other outcomes be failures for each roll. What is the probability of

(a)     Getting the sequence (FSFFFSF)? (7 points)

(b)    Getting at least three 2s in 5 rolls? (7 points)

(c)     Getting a 2 for the first time, on either the sixth, seventh, or eighth roll? (6 points)