Download First Fall 2000

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First Exam – QM 220 - Fall 2000/2001
[1] Answer the following questions by choosing the right answer:
1)
When samples are taken from a normally distributed population, the sampling distribution of
the sample mean (i.e. x ) has a normal distribution:
n
 0.05
a) if n  30
c) if

b) always
d) if x equals µ
2)
Two independent events:
a) have the same probability
b) have no effect on the probability of occurrence of each other
c) one of them is the complement to the other
d) cannot occur together
3)
Two independent events are:
a) always mutually exclusive
b) always complementary
c) never mutually exclusive
d) none of the above
4)
The mean and standard deviation of a binomial distribution with n=25 and p=0.2 are:
a) 5 and 4
c) .16 and 4
b) 25 and 4
d) 5 and 2
5)
The binomial probability distribution is symmetric if:
a) p < .5
c) p = .5
b) p > .5
d) none of the above
6)
Which of the following is not a characteristic of the normal distribution:
a) The total area under the curve is 1.0
b) The curve is symmetric about the mean
c) The two tails of the curve extend indefinitely
d) The value of the mean is always greater than the value of the standard deviation
7)
The z value for µ (population mean) for a normal curve is always:
a) positive
c) negative
b) zero
d) one
8)
Usually the normal distribution is used as an approximation to the binomial distribution if:
a) n ≥ 30
c) n p > 5 and n q > 5
b) n > 20 and p = 0.5
d) only if p equals q
9)
The mean of the sampling distribution of x is always equal to:
a) µ - σ
c) µ
b) 
d) SD
n
n
10) The standard deviation of the sampling distribution of the x decreases when:
a) x increases
c) n increases
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b) n decreases
d) x decreases
[2] The following table gives a two-way classification of 1000 workers selected from a large city:
COVERED by health
insurance ( C )
NOT COVERED by
health insurance
(C)
(M)
490
160
WOMEN ( M )
220
130
MEN
I)
If one worker is selected at random from this group, find the probability that this worker
is:
a) not covered by health insurance
b) a woman
c) a man given he is covered by health insurance
d) not covered by health insurance and is a man
e) covered by health insurance or is a woman
II)
Are the events “woman” and “not covered by health insurance” mutually exclusive?
Why?
III) Are the events “covered by health insurance” and “man” independent? Why?
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[3] A computer company buys 55% of all compute chips from company “A” and 45% from company
“B”. It is known that 1% of all the computer chips received from company “A” are defective, and
2% of all the computer chips received from company “B” are defective. Draw the probability
Tree .
One computer is found to contain a defective chips. What is the probability that this chip came
from company “B”.
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[4] At a food products company, a machine is used to fill 500 grams boxes of complete cereal.
The
net amount of cereal in all such boxes has a normal distribution with mean of 500 grams and
standard deviation of 8 grams:
a) What percentage of the boxes contains less than 483 grams of cereal?
b) What percentage of the boxes contains 507 to 517 grams of cereal?
c) What is the net weight of a cereal box so that (about) 10% of all cereal boxes have their
net weight more that this weight?
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