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fMath 227
Test #2
Name: __________________________
Show all necessary work for full credit. You may use graphing calculators for your calculation, but you
must show all detail and use the proper notations. Total is 100 points (with 5 bonus points).
1.
(20; 4ea)
The table lists the drinking habits of a group of college students.
Gender
Non-drinker
Regular drinker
Heavy drinker
Man
135
49
5
Women
187
21
8
If a student is chosen at random, find the probability of getting someone:
a. Who is a man or a non-drinker.
b. Who is a regular drinker.
c. Who is a heavy drinker given that the student is a woman.
d. Who is a women given that the student is a heavy drinker.
e. If two students are chosen at random, find the probability of getting both men.
2.
(4)
How many distinct arrangements can be formed from all the letters of “statistics”?
1
3.
Use the standard normal distribution table to find the following. For each, draw the diagram (density
curve).
a. PZ  3.15
c. P1.80  Z  2.08
(12)
d. PZ  c  0.0643 , find c.
b. PZ  2.56 or Z  2.56
4.
The latest poll shows that 47% will vote for Obama in the 2012 Presidential Election.
a. (3)Of 50 voters, find the expected number of votes for Obama.
(Total: 7)
b.
5.
(4)
(4)
Find the probability that, of 15 votes, at least 5 of them will be for Obama.
Let P(A) = 0.54, P(B) = 0.79, and P(AB) = 0.93. Find P(AB).
2
6.
(8)
Women’s heights are normally distributed with mean 63.6 in. and standard deviation 2.5 in.
a. (4)Find the probability that a randomly selected woman has a height that greater than 61 in.
b.
(4)If
an Exclusive club is only for the tallest 1% of women, what should be the cut off heights?
7.
(4)
Let P(A) = 48%, P(B) = 80%, and P(B|A) = 75% . Find P(AB).
8.
(5)
In a batch of 8000 clock radios 4% are defective. A sample of 15 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?
3
9.
(5)
License plates in a particular state display 3 letters followed by 3 numbers. How many different license
plates can be form if the first letter must be an K, L, or M and repetitions of letters and numbers is not
allowed?
10. (5) The local police department receives an average of two calls per hour. Find the probability that in a
randomly selected hour the number of calls is four.
11. (5) A 25-years old man pays $165 for a one-year life insurance policy with coverage of $150,000. If the
probability that he will live through the year is 0.9994. What is the expected value for the insurance
policy?
12. (8) You are taking a multiple-choice test that has 12 questions. Each of the questions has 5 choices, with
one correct choice per question. If you select one of these options per question and leave nothing black
a. in how many ways can you answer the questions.
b. What is the probability that you answered 8 of the 12 questions correctly?
4
13. (Total 12) A box
contains 4 quarters, 3 dimes, and 2 nickels.
a. (4) Two coins are selected at random without replacement one at a time. Compute the probability that the
first coin is a dime and the second is a nickel.
Three coins are selected at random with replacement. Compute the probability that at least one of them
is a nickel.
b.
(4)
c.
(4 ) Three
coins are selected without replacement, what is the probability of getting exactly 2 quarters?
14. (6) Find the mean and standard deviation of the probability distribution.
X
1
2
3
4
5
P(x)
0.1
0.2
0.3
0.3
01
5