Sample Test 2
Math 1107
DeMaio
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Create a probability model for the random variable.
1) A carnival game offers a $80 cash prize for anyone who can break a balloon by throwing a dart at
it. It costs $5 to play and you're willing to spend up to $20 trying to win. You estimate that you
have a 8% chance of hitting the balloon on any throw. Create a probability model for the amount
you will win. Assume that throws are independent of each other. Round to four decimal places if
necessary.
$75 $70
$65
$60
-$20
A) Amount won
P(Amount won) 0.08 0.0736 0.0677 0.0623 0.0573
Amount
won
$80 $75
$70
$65
-$20
B)
P(Amount won) 0.08 0.0736 0.0677 0.0623 0.0573
$75 $70
$65
$60
C) Amount won
P(Amount won) 0.08 0.0736 0.0677 0.7787
$80 $75
$70
$65
-$20
D) Amount won
P(Amount won) 0.08 0.0736 0.0677 0.0623 0.7164
$75 $70
$65
$60
-$20
E) Amount won
P(Amount won) 0.08 0.0736 0.0677 0.0623 0.7164
1)
Find the indicated probability.
2) The probability that Luis will pass his statistics test is 0.40. Find the probability that he will fail his
statistics test.
A) 2.50
B) 0.60
C) 0.67
D) 0.20
3) Suppose that in a certain population 8% of people are color blind. A researcher selects people at
random from this population. What's the probability that the first color blind person will be found
among the first 4 people checked?
A) 0.0623
B) 0.0573
C) 0.7787
D) 0.2836
B) 0.234
C) 0.486
D) 0.114
B) 0.5
C) 0.25
D) 0
B) 0.2278
C) 0.0076
D) 0.1139
B) 0.125
C) 0.382
D) 0.882
1
6)
E) 0.0188
7) You are dealt a hand of three cards, one at a time. Find the probability that you have at least one
red card.
A) 0.875
5)
E) 0.333
6) Suppose that 11% of people are left handed. If 6 people are selected at random, what is the
probability that exactly 2 of them are left handed?
A) 0.0121
4)
E) 0.222
5) You draw a card at random from a standard deck of 52 cards. Find the probability that the card is a
heart given that it is black.
A) 0.077
3)
E) 0.7164
4) A group of volunteers for a clinical trial consists of 81 women and 77 men. 18 of the women and 19
of the men have high blood pressure. If one of the volunteers is selected at random find the
probability that the person has high blood pressure given that it is a woman.
A) 0.513
2)
E) 0.118
7)
8) You are dealt a hand of three cards, one at a time. Find the probability that your cards are all
diamonds.
A) 0.231
B) 0.750
C) 0.705
D) 0.016
8)
E) 0.013
9) A sample of 100 wood and 100 graphite tennis rackets are taken from the warehouse. If 12 wood
and 13 graphite are defective and one racket is randomly selected from the sample, find the
probability that the racket is wood or defective.
9)
A) 0.125
B) 0.56
C) 0.565
D) There is insufficient information to answer the question.
Solve the problem.
10) Suppose that 12% of people are left handed. If 27 people are selected at random, what is the mean
of the number of right-handers in the group?
A) 3.24
B) 2.85
C) 13.5
D) 1.69
E) 23.76
11) A survey revealed that 31% of people are entertained by reading books, 39% are entertained by
watching TV, and 30% are entertained by both books and TV. What is the probability that a person
will be entertained by either books or TV?
A) 0.30
B) 0.40
C) 0.22
D) 0.70
B) 314
C) 0.190
D) 0.663
B) 0.0046
C) 0.0069
12)
E) 0.147
13) A study of the amount of time it takes a mechanic to rebuild the transmission for a 1992 Chevrolet
Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics
are randomly selected, find the probability that their mean rebuild time exceeds 9.1 hours.
A) 0.1285
11)
E) 1
12) An Imaginary Poll in April 2005 asked 933 U.S. adults what their main source of news was:
newspapers, television, internet, or radio? Here are the results:
Response
Number
Newspapers 244
Television 375
Internet
137
Radio
177
Total
933
If we select a person at random from this sample of 933 adults, what is the probability that the
person responded "Internet" or "Radio"?
A) 0.337
10)
13)
D) 0.1046
Solve.
14) Suppose that in one city, 83% of cars parked at meters still have time remaining on the meter. How
many cars should a meter maid expect to check before finding one at an expired meter?
A) 5.88
B) 83
C) 0.83
D) 17
14)
E) 1.2
Solve the problem. Round your answer, as needed.
15) A study conducted at a certain college shows that 75% of the school's graduates find a job in their
chosen field within a year after graduation. Find the probability that 5 randomly selected graduates
all find jobs in their chosen field within a year of graduating.
A) 0.2373
B) 0.3750
C) 0.0667
2
D) 3.7500
15)
Find the specified probability, from a table of Normal probabilities.
16) Based on past experience, a bank believes that 4% of the people who receive loans will not make
payments on time. The bank has recently approved 300 loans. What is the probability that over 6%
of these clients will not make timely payments?
A) 0.096
B) 0.038
C) 0.904
D) 0.962
16)
E) 0.017
17) The number of hours per week that high school seniors spend on homework is normally
distributed, with a mean of 10 hours and a standard deviation of 3 hours. 60 students are chosen at
17)
random. Let y represent the mean number of hours spent on homework for this group. Find the
probability that y is between 9.8 and 10.4.
A) 0.080
B) 0.5161
C) 0.3043
D) 0.1528
E) 0.547
Describe the indicated sampling distribution model.
18) Based on past experience, a bank believes that 8% of the people who receive loans will not make
payments on time. The bank has recently approved 600 loans. Describe the sampling distribution
model of the proportion of clients in this group who may not make timely payments.
18)
A) Binom(600, 8%)
B) There is not enough information to describe the distribution.
C) N(92%, 1.1%)
D) N(8%, 1.1%)
E) N(8%, 0.3%)
19) Suppose that the national mean weight for a three-year-old girl is 30 pounds with a standard
deviation of 3 pounds. A pediatric office takes a random sample of 100 three-year-old girls,
records their weights, and finds the mean. Describe the sampling distribution model of this mean.
19)
A) Binom(30, 3)
B) N(30, 0.03)
C) N(30, 3)
D) N(30, 0.3)
E) There is not enough information to describe the distribution.
Answer the question.
20) In a large class, the professor has each person toss a coin 200 times and calculate the proportion of
his or her tosses that were tails. The students then report their results, and the professor records
the proportions. One student claims to have tossed her coin 200 times and found 60% tails. What
do you think of this claim? Explain your response.
20)
A) This is a typical result. Her proportion is only 2.00 standard deviations above the mean.
B) This is a fairly unusual result. Her proportion is about 2.83 standard deviations above the
mean.
C) This is a fairly unusual result. Her proportion is about 2.00 standard deviations above the
mean.
D) This is a typical result. Her proportion is only 2.83 standard deviations above the mean.
E) This is an extremely unlikely result. Her proportion is about 200 standard deviations above
the mean.
21) What is the probability of an event that is certain to occur?
A) 1
B) 0.95
C) 0.5
3
21)
D) 0.99
In a large class, the professor has each person toss a coin several times and calculate the proportion of his or her tosses
that were heads. The students then report their results, and the professor plots a histogram of these several proportions.
Use the 68-95-99.7 Rule to provide the appropriate response.
22) If the students toss the coin 200 times each, about 68% should have proportions between what two
numbers?
22)
A) 0.34 and 0.67
B) 0.035 and 0.07
C) 0.465 and 0.535
D) 0.4975 and 0.5025
E) 0.16 and 0.84
Find the expected value of the random variable.
23) Your soccer team, Mill Valley, plays two games against Fairfield soccer team . The probability that
your team wins the first game is 0.6. If your team wins the first game, the probability that they also
win the second game is 0.7. If your team loses the first game, the probability that they win the
second game is 0.5.
Let the random variable X be the number of games won by your team, Mill Valley. Find the
expected value of X.
A) m = 1.22
B) m = 1.04
C) m = 1.02
D) m = 1.30
E) m = 1.10
24) Suppose you pay $3.00 to roll a fair die with the understanding that you will get back $5.00 for
rolling a 4 or a 1, nothing otherwise. What is the expected amount you win?
A) -$3.00
B) -$1.33
C) $-0.33
4
D) $5.00
23)
E) $3.00
24)
Answer Key
Testname: SAMPLE TEST 2 SUMMER 2010
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