Download Name Period Chapter 8 Review Special Topics Isabel Briggs Myers

Name __________________________________
Period _____________________
Chapter 8 Review
Special Topics
1.
Isabel Briggs Myers was a pioneer in the study of personality types. The personality types are broadly defined
accord to four main preferences. Do married couples choose similar or different personality types in the
mates? The following is the distribution of similar preferences:
Number of Similar Preferences
Probability
a.
b.
c.
d.
All four
Three
Two
One
.09
.35
.33
.19
What is the probability that a married couple
What is the probability that a married couple
What is the probability that a married couple
ways to make this calculation.
What is the probability that a married couple
None
?
had no preferences in common?
had no more than two preferences in common?
had at least two preferences in common? Name two
had either all four or no preferences in common?
2.
Three friends (A, B, and C) will participate in a round-robin tournament in which each one plays both of the
others. Suppose that P(A beats B) = .7, P(A beats C) = .8, and P(B beats C) = .6 and that the outcomes of the
matches are independent.
a. What is the probability that A wins both her matches?
b. What is the probability that A wins both her matches and B beats C?
c. What is the probability that A loses both her matches?
d. What is the probability that each person wins exactly one match?
3.
Suppose that for a group of consumers, the probability of eating pretzels is .75 and that the probability of
drinking Coke is .65. Further suppose that the probability of eating pretzels and drinking Coke is .55.
What is the probability of a person eating a pretzel or drinking a Coke?
4.
A randomly selected student is asked to respond yes, no, or maybe to the question, “Do you intend to vote in
the next presidential election?” The sample space is {yes, no, maybe}. Which of the following represents a
legitimate assignment of probabilities for this sample space?
a. .3, .3, .3
b. .4, .6, .4
c. .4, .4, .2
d. .5, .3, -.2
e. None of the above
5.
License plates in Florida have the form A12BCD, that is, a letter followed by two digits followed by three more
letters.
a.
b.
c.
How many possible different license plates are there?
Jerry would like a plate that ends in AAA. How many such plates are there?
If license plates are issued at random from all possible plates, what is the probability that Jerry will
get a plate that ends in AAA?
6.
An insurance company charges $800 annually for car insurance. This policy specifies that the company will pay
$1000 for a minor accident and $5000 for a major accident. If the probability of a motorist having a minor
accident during the year is .2, and of having a major accident is .05, what is the mean of this model? Will this
company make a profit in the long run?
7.
The mean income per household in a certain state is $9500 with a standard deviation of $1750. The middle
95% of incomes are between what two values?
8.
9.
A club has 25 members.
a.
How many ways are there to choose four members of the club to serve on an executive committee?
b.
How many ways are there to choose a president, vice president, secretary, and treasurer of the club?
Robert has 8 pairs of pants, 16 shirts, 9 pairs of socks, and 4 pairs of shoes. How many outfits can he
assemble?
10. If the first 2 symbols in a license tag are letters of the alphabet and the next 4 symbols are digits of our
numeral system, how many different tags can be made
a)
if no symbol may be repeated,
b)
if any symbol may be repeated?
11. Choose a person age 19 to 25 years at random and ask, “In the past four days, how many days did you do
physical exercise or work out?”
Based on a large sample survey, here is a discrete probability model for the answer you will get:
a.
b.
c.
What is the probability that the person you choose worked out either two or three days in the past four?
What is the probability that the person you choose worked out at least one day in the past four?
What is the mean and the standard deviation of this model?
12. The Iowa Test vocabulary scores of seventh-grade students in Gary, Indiana shows that the normal
distribution with mean μ = 6.8 and standard deviation σ = 1.6. Use the Empirical Rule to find the probability
that a randomly chosen student has a score:
a.
higher than 8.4.
b.
between 3.6 and 8.4.
c.
less than 6.8.
d.
at least 10.
e.
between 5.2 and 6.8
f.
less than 11.6
13. Explain how Caesar’s Palace casino can stay in business when just yesterday a gambler won $1,000,000.
14. The graph shows an unusual density curve. Find the proportion of observations within the following intervals.
a) 0.4  X  0.8
2
b) 0  X  0.4
1
c) 0.6  X  0.8
0
.2
.4
.6
.8
15. The manager of a large department with three floors reports that the time a customer on the second floor
must wait for an elevator has a uniform distribution ranging from 0 to 4 minutes.
a)
Draw and label this uniform distribution.
b)
Find the mean of x, the average time a customer on the second floor waits for an elevator.
c)
Find the probability that a randomly selected customer waits less than 1.5 minutes after pushing the
second-floor elevator button. Find it for more than 3.2 minutes, and for between 1 and 3 minutes.
16. In a population of students, the number of calculators owned is a random variable X with P(X = 0) =.2,
P(X = 1) = .45, and P(X = 2) = .15, P(X = 4) = .05. No student owns more than 4 calculators.
a)
What is the probability that a randomly selected student from this population would own exactly 3
calculators?
b)
If a student is selected at random from this population, what is the probability that he will have at least
one calculator?
c)
What is the expected number of calculators owned?