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MNS205 – HOMEWORK #9
9-1. In a family with 3 children, excluding multiple births, what is the probability of
having 2 boys and 1 girl, in that order? Assume that a boy is as likely as a girl at
each birth.[5 POINTS]
9-2. In a family with 3 children, excluding multiple births, what is the probability of
having 2 boys and 1 girl, in any order? Assume that a boy is as likely as a girl at
each birth.[5 POINTS]
9-3. An experiment consists of rolling two fair dice and adding the dots on the two sides
facing up. Using the sample space shown in Figure 2 (textbook p. 389) and
assuming each simple event is as likely as any other, find the probability that the
sum of the dots is not 2, 4, or 6.[5 POINTS]
9-4. In a lottery game, a single ball is drawn at random from a container that contains 25
identical balls numbered from 1 – 25. Compute the probability that the number
drawn is less than 6 or greater than 19.[10 POINTS]
9-5. Use the equally likely sample space in Example 2 (textbook p. 401) to compute the
probability of the following outcome when rolling a pair of dice: The number on
the first die is even or the number on the second die is even.[10 POINTS]
9-6. a. Construct a frequency table and histogram for the following data set using a class
interval width of 1, starting at 0.5. [15 POINTS]
DATA: 6, 7,2, 7, 9, 6, 4, 7, 6, 6
b. Construct a frequency table and histogram for the following data set using a
class interval width of 1, starting at 0.5. [15 POINTS]
DATA: 5, 6, 8, 1, 3, 5, 10, 7, 6, 8
c. How are the histograms of parts (a) and (b) different?[10 POINTS]
9-7. Gasoline Tax. Find the mean, median, and mode for the data in the following
table.[15 POINTS]
State Gasoline Tax, 2007
State
Tax (Cents)
Wisconsin
32.9
New York
44.5
Connecticut
Nebraska
Kansas
Texas
California
Florida
35.5
26.2
25
20
41.6
31.1
9-8. Find the standard deviation the following sample data using formula (4) (textbook
p. 543.[10 POINTS]
1, 1, 1, 1, 2, 3, 4, 5, 5, 5
9-10. Solve the following linear programming problem.
Maximize
P = 30x + 40y
subject to
2x + y ≤ 10
x + y ≤ 7
x + 2y ≤ 12
x, y ≥ 0
[20 POINTS]
9-11. A county park system rates its 20 golf courses in increasing order of difficulty
as bronze, silver, or gold. There are only two gold courses and twice as many
bronze as silver courses.
a. If a golfer decides to play a round at a silver or gold course, how many
selections are possible? [5 POINTS]
b. If a golfer decides to play one round per week for 3 weeks, first on a bronze
course, then silver, then gold, how many combined selections are possible?
[5 POINTS]