Spring2009
Math 227 Test #2(Ch4, Ch5, Ch6) Name: ___________________________
Show all necessary work NEATLY, UNDERSTANDABLY and SYSTEMATICALLY for full points.
Any understatement and/or false statement may be penalized. This is a closed book, closed note
and closed neighborhood test. If you are using a TI calculator, you must write down exactly what
was input to the calculator. Total is 100 points. Good Luck!
1. <18 points:3 ea.> The table below describes the smoking habits of a group of asthma sufferers.
Nonsmoker
Light Smoker
Heavy smoker
395
405
100
Men
300
680
120
Women
a. If one person is randomly selected, find the probability that the person chosen is a
nonsmoker.
b. If one person is randomly selected, find the probability that the person chosen is a nonsmoker
given that the person is a woman.
c. If one person is randomly selected, find the probability that the person chosen is a man or a
heavy smoker.
d. If one person is randomly selected, find the probability that the person chosen is a man given
that the person a nonsmoker.
e. If one person is randomly selected, find the probability that the person chosen is a
nonsmoking man.
f. If two people are randomly selected, find the probability that they are both light smokers.
2.
(6 points) Among the contestant in a competition are 49 women and 29 men. If 5 winners are
randomly selected, what is the probability that they are all men?
3.
(6 pts)
In a batch of 8000 clock radios 6% are defective. A sample of 5 clock radios is randomly
selected without replacement from the 8000 and tested. The entire batch will be rejected if at
least one of those tested is defective. What is the probability that the entire batch will be
rejected?
4.
(6 pts)
5.
(8 points)
A computer salesman averages 0.9 sales per week. Find the probability that in a randomly
selected week the number of computers sold is 1.
Two fair dice are rolled.
a. Find the probability of obtaining a double or sum is 10.
b. Find the probability that the sum is 6, given a double showed up.
6.
The Denver Post reported that a recent audit of the Los Angeles 911 calls showed that 85%
were not emergencies. Suppose that the 911 operators in Los Angeles have just received five
calls.
a. What is the probability that all five calls are in fact emergencies? Would it be unusual to
receive all five emergency calls?
(8 pts)
b. Find the expected number of calls that are emergencies? What is the standard deviation?
7.
In a certain town, 20% of adults have a college degree. The accompanying table
describes the probability distribution for the number of adults (among 4 randomly selected
adults) who have a college degree.
X
P(x)
0
0.4096
1
0.4096
2
0.1536
3
0.0256
4
0.0016
(12 pts: 4 ea.)
a. Find the mean.
b. Find the standard deviation.
c. Find the probability that at most 3 adults have a college degree.
8.
A bag contains 8 red marbles, 3 blue marbles, and 1 green marble.
a. If one marble is randomly selected, what is the probability of selecting a marble that is
not blue?
(9 pt: 3, 4ea.)
b. If two marbles are randomly selected without replacement, what is the probability of
selecting two red marbles?
c. If 3 marbles are randomly selected without replacement, what is the probability of
selecting 1 red and 2 blue marbles?
9.
(15pts: 3ea)
Find the following probability. For each problem, draw the normal curve and shape the
area.
a. P( z  1.52)
b. P(0.75  z  2.03)
c. P( z  0.67)
d. P(z < -2.57 or z > 2.57)
e. If P(0<z<a) = 0.3907, find a.
10. (6 pts) Assume that adults have IQ scores that are normally distributed with a mean of 100 and a
standard deviation of 15. Find the probability that a randomly selected adult has an IQ greater
than 115.5.
11. (6 pts) Scores for men on the verbal portion of the SAT-I test are normally distributed with a mean
of 509 and a standard deviation of 112. If 16 of the men are randomly selected, find the
probability that their mean score is at least 550.