MATH 333:Probability & Statistics. Exam 1 (Fall 2003) Scores
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October 8, 2003 (A) NJIT
Instructors M. Bhattacharjee, S. Dhar, R. Dios, A. Jain, K. Johnson, K. Rappaport,
T. Spencer
č Must show all work to receive full credit.
I
pledge my honor that I have abided by the Honor System. ___________________
(Signature)
1. The following data are the
joint temperatures of the Orings (^{ 0}F) 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. 129131):
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 Stemand 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(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 nondefective 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)