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MATH 156, General Statistics
Test 2
Devore & Peck, Ch. 5-7
February 25, 2000
Name____________________________________
1. Suppose that an ordinary fair die has four faces painted blue and two painted red. It is
tossed twice. Find the probability that
a) both tosses are red _________
b)at least one is blue ____________
c) exactly one is blue _____________
2. The 200 members of a student organization were asked about their reaction to a
reorganization proposal. Their numbers who responded positively and negatively and
their class are summarized below.
Yes
No
Freshmen
50
40
Sophomores
30
30
Juniors
20
5
Seniors
20
5
Find the probability that a club member chosen at random is a freshman __________
b) is not a freshman _________ c) is a junior who voted yes ___________
d) is either a junior or a person who voted yes _____________.
3. A machine cuts a length of string anywhere up to 8 inches. Find the probability that a
piece chosen at random is
a) less than 5 inches_________ b) no more than 5 in._____
c) between 2 in. and 7 in. _____________
d) both of two independently chosen pieces are less than 2 in __________
e) What would you expect the mean length to be? _______________.
MATH 156, Test 2, 2/25/00, page 2
4. The probability distribution for the number of games, X, in a World Series between
evenly matched teams is given below.
X
4
5
6
7
P(X)
.125
.25
.3125
.3125
Find the probability that a) X > 5 _________
b) X > 5________, c) X is even __________
d) Find the mean number of games ________
5. Comment on the appropriateness of taking a sample in one city neighborhood in
order to estimate the support for a statewide bond issue.
6.
Suppose that the scores on a college entrance test are scaled to be normally
distributed with mean 200 and standard deviation 50. Find the probability that a test
chosen at random has score
a) between 170 and 230 _____ b) above 230 _________ c) below 170_______
d) Find the score exceeded by only 2% of all scores ______________-
7. If a sample of 25 scores is randomly chosen from the test described in problem 6, and
the sample mean computed, find the probability that the sample mean is
a) between 170 and 230 ______ b) above 230 ________ c)below 170________
.
d) Find the mean exceed only 2% of the time. ____________
MATH 156, Test 2, 2/25/00, page 3
8. Suppose that the mean time to complete a task by skilled workers is 12.5 min. with a
standard deviation of 2 min. Suppose a sample of 100 skilled workers is observed
and their mean completion time computed.
a) Find the mean of the population of mean times. ____________
b) Find the standard deviation of the population of mean times. _________
c) What can be said about the probability distribution of those mean times? Justify
your answer.
9. How would the answers to all three parts of problem 8 be changed if the sample size
was 25?
10. A coin is bent so that the probability of heads is .4. It is tossed 96 times and the
sample proportion if heads, p, observed.
a) What is the mean value for p? ______________
b) Find the standard deviation for the population of all such proportions. ________
c) What can be said about the probability distribution for p? Justify your answer.
d) Find the probability that .3 < p < .5 ___________
e) How large must the sample be in order to be assured that the normal probabilities
will apply?