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AP Stats
Name_______________________
1. A crop insurance company establishes the following loss table based upon previous claims.
Find x.
% loss
P(x)
0
0.9
25
0.05
50
0.02
100
x
2. Given the following probability distribution for the # of defects a day.
#defects
P(x)
0
0.12
1
0.18
2
0.28
3
0.31
4
0.11
a. Find  x .
c. Find P( x  3) .
b. Find  x .
d. Find P (2  x  4) .
3. Two companies make the same product. Steve buys from both. What is the probability
that he buys a batch from Company A with two defects and a batch from Company B with
two defects.
Company A
#defects
P(x)
0
0.3
1
0.38
Company B
2
0.26
3
0.05
#defects
P(x)
0
0.2
1
0.31
2
0.24
3
0.19
4. A rock concert producer has scheduled an outdoor concert. If it is warm that day, she
expects to make a $20,000 profit. If it is cool that day, she expects to make a $5000
profit. If it is very cold that day, she expects to suffer a $12,000 loss. Based upon
historical records, the weather office has estimated the chances of a warm day to be
0.60; the chances of a cool day to be 0.25. what is the producer’s expected profit?
5. Mary can choose between 2 payment plans. In plan A, Mary will earn $160 per week. In
plan B, Mary will earn $100 per week and $20 per sale. The distribution of sales per week
is shown. Which plan should Mary choose?
# sales
P(x)
0
0.08
1
0.16
2
0.32
3
0.25
4
0.14
5
0.05
6. The probability that a certain machine will produce a defective item is ¼. If a random
sample of 6 items is taken from the output of this machine, what is the probability that
there will be 3 defective items?
7. If you buy one ticket in the Lottery, then the probability that you will win a prize is 0.11.
If you buy one ticket each month for eight months, what is the probability that you will
win
a. at least 2 prizes?
b. exactly 1 prize?
c. at most 3 prizes?
8. The probability of Joe passing his driver’s test is 0.20.
a. Find the probability that he will have not passed the test until the 4th try?
b. Find the probability that it will take less 3 times until he passes the test?
9. One of the side effects of flooding a lake in northern boreal forest areas is that mercury
is leached from the soil, enters the food chain, and eventually contaminates the fish. The
concentration in fish will vary among individual fish. Suppose that the concentrations of
mercury in individual fish follows an approximate normal distribution with a mean of 0.25
ppm and a standard deviation of 0.08 ppm. Fish are safe to eat if the mercury level is
below 0.30 ppm. What proportion of fish are safe to eat?
10. Suppose the test scores of 600 students are normally distributed with a mean of 76 and
standard deviation of 8. The number of students scoring between 70 and 82 is what?
11. If the mean of a test is 89 with standard deviation of 3.2, find the score that represents
the 80th percentile?
12. the diameters of steel disks produced in a plant are normally distributed with a mean of
2.5 cm and standard deviation of 0.02 cm. The probability that a disk picked at random
has a diameter greater than 2.54 cm is about what?
13. A standardized test has 24.3% of the people score less than 82 and 32% score more
than a 87, find the mean and standard deviation.