MATH 333:Probability & Statistics.  Exam 1 (Fall 2003)                                              Scores

 #1 # 2 #3 #4 #5 #6 Total

October 8, 2003 (A)          NJIT

Instructors M. Bhattacharjee, S. Dhar, R. Dios, A. Jain, K. Johnson, K. Rappaport, T. Spencer

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1. The following data are the joint temperatures of the O-rings ( 0F) for each test firing or actual launch of the space shuttle rocket motor (from Presidential Commission on the Space Shuttle Challenger Accident, Vol. 1, pp. 129-131):

84, 49, 61, 40, 83, 67, 45, 66, 70, 69, 80, 58, 68, 60, 67, 72, 73, 70, 57, 63, 70, 78, 52, 67, 53, 67, 75, 61, 70, 81, 76, 79, 75, 76, 58, 31.

(a)    Construct a Stem-and Leaf diagram of the temperature data. (12 pts)

(a)    What is the median of the data? (6 pts)

(b)   Are there any unusual points (i.e. possible outliers)? (6 pts)

2. Let A and B be two events and the following are given:

# P(A) = 0.6

P(B) = 0.7

P(A˘∩B˘) = 0.2. (4 pts each)

(a)    Find P(AUB)

(b)   Find P(A∩B)

(c)    Find P(A˝B)

(d)   Find P(B˝A)

3. The probability that a customer’s order is not shipped on time is 0.05.  A particular customer places 3 orders, and the orders are placed far enough apart in time that they can be considered to be independent events. (6 pts each)

(a)    What is the probability that all are shipped on time?

(b)   What is the probability that exactly one is not shipped on time?

(c)     What is the probability that two or more orders are not shipped on time?

4. A production facility employs 20 workers on the day shift, 12 workers on the swing shift and 8 workers on the night shift. A consultant wants to select 6 of the workers for interviews. (6 pts each)

(a)    Find the probability that all 6 are from the day shift.

(b)   Find the probability that all 6 workers are from the same shift.

5. One percent (1%) of all items produced by a manufacturing company are defective (i.e., do not meet the product specifications). A quality control inspector works for the company to identify the defective items. Items that are defective are correctly so identified by the inspector with a probability of 0.99; while items that meet product specifications are correctly identified as non-defective with a probability of 0.995. (9 pts each)

(a)    What is the probability that a randomly selected item will be classified by the inspector as defective?

(b)   What is the probability that an item classified as defective by the inspector is actually one that conforms to the product specifications?

6. A bridge hand consists of any 13 cards selected from a 52 - card deck without regard to order.  There are four suits (hearts, diamonds, clubs and spades). Each suit consists of 13 cards. Find the probability of getting a bridge hand of only spades and hearts with both suits represented in the
hand. (12 pts)