Unit 6 MC

Question 1

According to CBS/ New York Times poll taken in 1992, 15% of the public have responded to a telephone call-in poll. In a random group of five people, what is the probability that exactly two have responded to a call-in poll?

Answer 1

0.138

Question 2

Alan Dershowitz, one of O.J. Simpson’s layers, has stated that only 1 out of every 1000 abusive relationships ends in murder each year. If he is correct, and if there are approximately 1.5 million abusive relationships in the United States, what is the expected value for the number of people who are killed each year by an abusive partner?

Answer 2

1500

Question 3

A television game show has three payoffs with the following probabilities:
Payoffs ($): 0 1000 10,000
Probability: .6 .3 .1
What are the mean and standard deviation for the payoff variable?

Answer 3

mean: 1300
standard deviation: 2934

Question 4

At a warehouse sale 100 customers are invited to choose one of 100 identical boxes. Five boxes contain $700 color television sets, 25 boxes contain $540 camcorders, and the remaining boxes contain $260 cameras. What should a customer be willing to pay to participate in the sale?

Answer 4

$352

Question 5

The average annual incomes of high school and college graduates in a midwestern town are $21,000 and $35,000, respectively. If a company hires only personnel with at least a high school diploma and 20% of its employees have been through college, what is the mean income of the company employees?

Answer 5

$23,800

Question 6

An insurance company charges $800 annually for car insurance. The 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, 0.5, how much can the insurance company expect to make on a policy?

Answer 6

$350

Question 7

You can choose one of three boxes. Box A has four $5 bills and a single $100 bill, box B has 400 $5 bills and 100 $100 bills, and box C has 24 $1 bills. You can have all of box C or blindly pick one bill out of either box A or box B. Which offers the greatest expected winning?

Answer 7

All offer the same expected winning

Question 8

Suppose you are one of 7.5 million people who send in their name for a drawing with 1 top prize of $1 million, 5 second-place prizes of $10,000, and 20 third-place prizes of $100. Is it worth the $0.44 postage it costs you to send in your name?

Answer 8

No, because your expected winnings are only $0.14.

Question 9

You have a choice of three investments, the first of which gives you a 10% chance of making $1 million, otherwise you lose $25,000; the second of which gives you a 50% chance of making $500,000, otherwise you lose $345,000; and the third of which gives you an 80% chance of making $50,000; otherwise you make only $1,000. Assuming you will go bankrupt if you don’t show a profit, which option should you choose for the best chance of avoiding bankruptcy?

Answer 9

Third choice

Question 10

Can the function f(x)= (x+6)/24 , for 1, 2, and 3, be the probability distribution for some random variable?

Answer 10

Yes

Question 11

Sixty-five percent of all divorce cases cite incompatibility as the underlying reason. If four couples file for a divorce, what is the probability that exactly two will state incompatibility as the reason?

Answer 11

0.311

Question 12

Suppose we have a random variable (X) where the probability associated with the value (10 ) (.37)^k (.63)^10-k
( k )
… for k=0,……., 10. What is the mean of X?

Answer 12

3.7

Question 13

Which of the following are true statements?
i. The histogram of a binomial distribution with p=.5 is always symmetric no matter what n, the number of trials, is.
ii. The histogram of a binomial distribution with p=.9 is skewed to the right.
iii. The histogram of a binomial distribution with p=.9 is almost symmetric if n is very large.

Answer 13

i and iii

Question 14

Companies proved to have violated pollution laws are being fined various amounts with the following probabilities:
fine ($): 1000. 10,000. 50,000. 100,000
prob.: .4 .3
.2 .1
What are the mean and standard deviation for the fine variable?

Answer 14

mean: 23,400
standard deviation: 31,350

Question 15

Which of the following lead to binomial distributions?
i. An inspection procedure at an automobile manufacturing plant involves selecting a sample of cars from the assembly line and noting for each car whether there are no defects, at least one major defect, or only minor defects.
ii. As students study more and more during their AP Statistics class, their chances of getting an A on any given test continue to improve. The teacher is interested in the probability of any given student receiving various numbers of A’s on the class exams.
iii. A committee of two is to be selected from among the five teachers and ten students attending a meeting. What are the probabilities that the committee will consist of two teachers, of two students, or of exactly one teacher and one student?

Answer 15

None of the above gives the complete set of true responses

Question 16

Which of the following is a true statement?
a) The area under a normal curve is always equal to 1, no matter what the mean and SD are
b) All bell shaped curves are normal distributions for some choice of mean and SD
c) The smaller the SD of a normal curve, the lower and more spread out the graph
d) Depending upon the value of the SD, normal curves with different means may be centered around the same number.
e) Depending upon the value of the SD, the mean and median of a particular normal distribution may be different.

Answer 16

a) The area under a normal curve is always equal to 1, no matter what the mean and standard deviation are

Question 17

Which of the following is a true statement?
a) The area under the standard normal curve between 0 and 2 is twice the area between 0 and 1.
b) The area under the standard normal curve between 0 and 2 is half the area between -2 and 2.
c) For the standard normal curve, the interquartile range is approx. 3
d) For the standard normal curve, the range is 6.
e) For the standard normal curve, the area of the left of 0.1 is the same as the area to the right of 0.9

Answer 17

b) The area under the standard normal curve between 0 and 2 is half the area between -2 and 2

Question 18

Populations P1 and P2 are normally distributed and have identical means. However, the standard deviation of P1 is twice the standard deviation of P2. What can be said about the percentage of observations falling between two standard deviations of the mean for each population?

Answer 18

The percentages are identical.

Question 19

Consider the following two normal curves:
- a is wide and short (range 0 to 12)
- b is thin and tall
(range 15 to 21)

Answer 19

Larger mean, b; larger standard deviation, a

Question 20

A trucking firm determines that its fleet of trucks averages a mean of 12.4 miles per gallon with a standard deviation of 1.2 miles per gallon on cross-country hauls. What is the probability that one of the trucks averages fewer than 10 miles per gallon?

Answer 20

0.0228

Question 21

A factory dumps an average of 2.43 tons of pollutants into a river every week. If the standard deviation is 0.88 tons, what is the probability that in a week more than 3 tons are dumped?

Answer 21

0.2578

Question 22

An electronic product takes an average of 3.4 hours to move through an assembly line. If the standard deviation is 0.5 hour, what is the probability that an item will take between 3 and 4 hours?

Answer 22

0.6730

Question 23

The mean score on a college placement exam is 500 with a standard deviation of 100. Ninety-five percent of the test takers score above what?

Answer 23

336

Question 24

The average noise level in a restaurant is 30 decibels with a standard deviation of 4 decibels. Ninety-nine percent of the time it is below what value?

Answer 24

39.3

Question 25

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?

Answer 25

$6070 and $12,930

Question 26

One company produces movie trailers with mean 150 seconds and standard deviation of 40 seconds, while a second company produces trailers with mean 120 seconds and standard deviation 30 seconds. What is the probability that two randomly selected trailers, one produced by each company, will combine to less than three minutes?

Answer 26

0.036

Question 27

Jay Olshansky from the University of Chicago was quoted in Chance News as arguing that for the average life expectancy to reach 100, 18% of the people would gave to live to 120. What standard deviation is he assuming for this statement to make sense?

Answer 27

21.7

Question 28

Cucumbers grown on a certain farm have weights with a standard deviation of 2 ounces. What is the mean weight if 85% if the cucumbers weigh less than 16 ounces?

Answer 28

13.92

Question 29

If 75% of all families spend more than $75 weekly for food, while 15% spend more than $150, what is the mean weekly expenditure and what is the standard deviation?

Answer 29

mean: 104.39
standard deviation: 43.86

Question 30

A coffee machine can be adjusted to deliver any fixed number of ounces of coffee. If the machine has a standard deviation in delivery equal to 0.4 ounce, what should be the mean setting so that an 8-ounce cup will overflow only 0.5% of the time?

Answer 30

6.97 ounces

Question 31

Assume that a baseball team has an average pitcher, that is, one whose probability of winning any decision is 0.5. If this pitcher has 30 decisions in a season, what is the probability that he will win at least 20 games?

Answer 31

0.0505

Question 32

Given that 10% of the nails made using a certain manufacturing process have a length less than 2.48 inches, while 5% have a length greater than 2.54 inches, what are the mean and standard deviation of the lengths of the nails? Assume that the lengths have a normal distribution.

Answer 32

The mean and standard deviation cannot be computed from the information given.

Question 33

Students are classified by television usage (unending, average, and infrequent) and how often they exercise ((regular, occasional, and never), resulting in the following joint probability table.
TV usage = x
- unending: 1
- average: 2
- infrequent: 3
Exercise = y
- regular: 1
- occasional: 2
- never: 3
1. 2. 3.
1. .05 .05 .10
2. .20 .15 .10
3. .15 .15 .05
What is the probability distribution for X?

Answer 33

P(X=1) = .20
P(X=2) = .45
P(X=3) = .35

Question 34

Students are classified by television usage (unending, average, and infrequent) and how often they exercise ((regular, occasional, and never), resulting in the following joint probability table.
TV usage = x
- unending: 1
- average: 2
- infrequent: 3
Exercise = y
- regular: 1
- occasional: 2
- never: 3
1. 2. 3.
1. .05 .05 .10
2. .20 .15 .10
3. .15 .15 .05
What is the probability P(X=2, Y=3), that is, the probability that a student has average television usage but never exercises?

Answer 34

.10

Question 35

Students are classified by television usage (unending, average, and infrequent) and how often they exercise ((regular, occasional, and never), resulting in the following joint probability table.
TV usage = x
- unending: 1
- average: 2
- infrequent: 3
Exercise = y
- regular: 1
- occasional: 2
- never: 3
1. 2. 3.
1. .05 .05 .10
2. .20 .15 .10
3. .15 .15 .05
What is the probability P(X=2|Y=3), that is, the probability that a student has average television usage given that he never exercises?

Answer 35

.40

Question 36

Students are classified by television usage (unending, average, and infrequent) and how often they exercise ((regular, occasional, and never), resulting in the following joint probability table.
TV usage = x
- unending: 1
- average: 2
- infrequent: 3
Exercise = y
- regular: 1
- occasional: 2
- never: 3
1. 2. 3.
1. .05 .05 .10
2. .20 .15 .10
3. .15 .15 .05
Are X and Y independent?

Answer 36

No.

Question 37

Suppose X and Y are random variables with E(X)=25, var(X)=3, E(Y)=30, var(Y)=4. What are the expected value and variance of the random variable X+Y?

Answer 37

E(X+Y) = 55
var(X+Y) = 7

Question 38

Suppose X and Y are random variables with mean(X)=10, SD(X)=3, mean(Y)=15, and SD(Y)=4. Given that X and Y are independent, what are the mean and standard deviation of the random variable X+Y?

Answer 38

mean(X+Y)= 25
standard deviation(X+Y)= 5

Question 39

Suppose X and Y are random variables with E(X)=500, var(X)=50, E(Y)=400, and var(Y)=30. Given that X and Y are independent, what are the expected value and variance of the random variable X-Y?

Answer 39

E(X-Y) = 100
var(X-Y) = 80

Question 40

Suppose the average height of policemen is 71 inches with a standard deviation of 4 inches, while the average for policewomen is 66 inches with a standard deviation of 3 inches. If a committee looks at all ways of pairing up one male with one female officer, what will be the mean and standard deviation for the difference in heights for the set of possible partners?

Answer 40

Mean of 5 inches with a standard deviation of 5 inches

Question 41

Consider the sets of scores of all students taking the AP Statistics exam. What is true about the variance of this set?
a) given a boxplot of this distribution, if the whisker lengths are equal, the variance will be the interquartile range.
b) if the distribution of scores is bell-shaped, the variance will be between -3 and +3
c) if there are a few high scores with the bulk of the scores less than the mean, the variance will be skewed to the right
d) if the distribution is symmetric, the variance will equal the standard deviation
e) the variance is the sum of variances coming from a variety of factors such as study time, course grade, IQ, and so on.

Answer 41

c). If there are a few high scores with the bulk of the scores less than the mean, the variance will be skewed to the right.

Question 42

The discrete random variable x = the number of 911 calls in a small town in one day has the following probability distribution:
x: 1 2 3 4 5 6
p: .2 .35 .15 .1 .1 .1
Which of the following could be evaluated to compute the mean of this probability distribution?
(A) 1+2+3+4+5+6 / 6
(B) 0.20+0.35+0.15+0.10+0.10+0.10 / 6
(C) 1(0.20) + 2(0.35) + 3(0.15) + 4(0.10) + 5(0.10) + 6(0.10)
(D) 1(0.20) + 2(0.35) + 3(0.15) + 4(0.10) + 5(0.10) + 6(0.10) / 6
(E) 1^2(0.20) + 2^2(0.35) + 3^2(0.15) + 4^2(0.10) + 5^2(0.10) + 6^2(0.10)

Answer 42

(C) 1(0.20) + 2(0.35) + 3(0.15) + 4(0.10) + 5(0.10) + 6(0.10)

Question 43

A college basketball game is made up of two 20-minute halves. Each half is 20 minutes of playing time, but the “real” time elapsed from the start of play to the end of the half is much longer. This is due to time-outs and other periods of time when the game clock is stopped. Suppose that the mean and standard deviation for the “real” time (in minutes) of each half are:
mean SD
1st half 48 6
2nd half 52 8
What is the mean “real” time for the entire game (1st half + 2nd half)?
a) 48
b) 50
c) 52
d) 100
e) 114

Answer 43

d) 100

Question 44

A college basketball game is made up of two 20-minute halves. Each half is 20 minutes of playing time, but the “real” time elapsed from the start of play to the end of the half is much longer. This is due to time-outs and other periods of time when the game clock is stopped. Suppose that the mean and standard deviation for the “real” time (in minutes) of each half are:
mean SD
1st half 48 6
2nd half 52 8
Under what conditions is the standard deviation of the total “real” game time (1st and 2nd half) equal to sqrt 6^2+8^2 = 10?
a) no conditions necessary - the SD will be 10 minutes
b) the SD will not be 10 minutes under any circumstances
c) the SD will be 10 minutes only if the 1st half “real” time is shorter than the 2nd half “real” time
d) the SD will be 10 minutes only if the “real” times in the two halves are independent
e) the SD will be 10 minutes only if the “real” times in the two halves are mutually exclusive

Answer 44

a) No conditions necessary - the standard deviation will be 10 minutes

Question 45

Ten percent of the students at a particular school own a pet. Consider the chance experiment that consists of selecting a random sample of 20 students from this university. Let x = the number of students in the sample who own a pet. The random variable x has which of the following probability distributions?
a) a binomial distribution
b) a geometric distribution
c) a normal distribution
d) a uniform distribution
e) none of the above

Answer 45

a) a binomial distribution

Question 46

Let x denote the number of accidents in a given month at a certain intersection. Suppose that the probability distribution of x is:
x. 0. 1. 2. 3. 4. 5.
p. 0.110. 0.215. 0.260. 0.214. 0.134. 0.067
If the numbers of accidents in any 2 months are independent, what is the probability that no car accidents occur at this intersection for 2 consecutive months?
a) 0.0121
b) 0.1100
c) 0.2200
d) 0.8900
e) none of the above

Answer 46

a) 0.0121

Question 47

A normal probability plot suggests that a normal probability model is plausible when:
a) no obvious patterns are present in the plot
b) a bell-shaped pattern is present in the plot
c) a substantial quadratic pattern is present in the plot
d) a substantial linear pattern is present in the plot
e) any of the above is present in the plot

Answer 47

a) no obvious patterns are present in the plot

Question 48

For a normally distributed population with a mean 0 and standard deviation 1.0, the population interquartile range is closest to which of the following values?
a) 0.50
b) 1.28
c) 1.349
d) 1.645
e) 1.96

Answer 48

c) 1.349

Question 49

Which of the following is not a property of a binomial experiment?
a) it consists of a fixed number of trials, n
b) outcomes of different trials are independent
c) each trial can result in one of several different outcomes
d) observations consist of the number of successes for each trial of the experiment
e) the probability of success is constant for each trial

Answer 49

c) each trial can result in one of several different outcomes

Question 50

Suppose that x has a probability distribution with density function f(x) = {c, if 6<x<8, 0 otherwise
The value of c is:
a) 0.5
b) 0.6
c) 0.7
d) 0.8
e) 0.9

Answer 50

a) 0.5

Question 51

The number of passengers who choose to check luggage on a flight from Los Angeles to San Francisco is a binomial random variable with n = number of passengers on the flight. If the probability that any individual passenger checks luggage is 0.3, what is the probability that exactly 40 of the 100 passengers on this flight on a particular day check luggage?
a) 0
b) 0.3
c) (0.3)^40
d) (0.3)^40 (0.7)^60
e) (100) (0.3)^40 (0.7)^60
( 40 )

Answer 51

e) (100) (0.3)^40 (0.7)^60
( 40 )

Question 52

Suppose that 65% of the students at a particular university have a Twitter account. If 100 students are selected at random from this university, what are the mean and standard deviation of the random variable x = number of selected students who have a Twitter account?
a) mean = 0.65, standard deviation = 0.35
b) mean = 0.65, standard deviation = 0.002
c) mean = 65, standard deviation = 22.75
d) mean = 65, standard deviation = 0.228
e) mean = 65, standard deviation = 4.770

Answer 52

e) mean = 65, standard deviation = 4.770

Question 53

Suppose that x is a random variable that has a uniform distribution over the interval from 0 to 10. Which of the following probabilities is largest?
a) p(x > 8)
b) p(x>_ 8)
c) p(x = 10)
d) p(3 < x < 6)
e) p (x < 4)

Answer 53

b) p(x>_8)

Question 54

Suppose that 20% of cereal boxes contain a prize and the other 80% contain the message “Sorry, try again.” Boxes of this cereal will be purchased and opened until a prize is found. Define the random variable x to be the number of boxes purchased. What is the probability that exactly three boxes must be purchased?
a) (0.20)^3
b) 0.8 + 0.8 + 0.2
c) (0.8)^2 + (0.2)
d) (0.8)^2 (0.2)
e) 3!/2!1! (0.8)^2 (0.2)^1

Answer 54

c) (0.8)^2 + (0.2)

Question 55

For a normal distribution with mean 100 and standard deviation 10, the 95th percentile is…
a) -1.645
b) 1.645
c) 16.45
d) 83.55
e) 116.45

Answer 55

e) 116.45