Final Exam
Math 1107
DeMaio
Name___________________________________
Each of the 22 questions is worh 5 points for a totla of 110 possible points.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the mean for the given sample data.
1) Six college buddies bought each other Christmas gifts. They spent:
$180.51 $124.98 $203.40
$285.53 $292.33 $241.68
What was the mean amount spent? Round your answer to the nearest cent.
A) $332.11
B) $265.69
C) $221.41
D) $253.69
Find the median for the given sample data.
2) The salaries of ten randomly selected doctors are shown below.
$117,000 $120,000 $190,000 $234,000 $228,000
$142,000 $122,000 $760,000 $219,000 $166,000
Find the median salary.
A) $230,000
B) $190,000
C) $256,000
D) $178,000
Find the range for the given data.
3) Fred, a local mechanic, gathered the following data regarding the price, in dollars, of an oil and filter change at
twelve competing service stations:
32.95 24.95 26.95 28.95
18.95 28.95 30.95 22.95
24.95 26.95 29.95 28.95
Compute the range.
A) $12
B) $10
C) $8
D) $14
Find the standard deviation for the given data. Round your answer to one more decimal place than the original data.
4) Christine is currently taking college astronomy. The instructor often gives quizzes. On the past seven quizzes,
Christine got the following scores:
52 20 126 24 20 55 55
Compute the standard deviation s.
A) 126
B) 37.2
C) 17,700.6
D) 26,006
Find the indicated probability.
5) The distribution of B.A. degrees conferred by a local college is listed below, by major.
Major
Frequency
English
2073
Mathematics
2164
Chemistry
318
Physics
856
Liberal Arts
1358
Business
1676
Engineering
868
9313
What is the probability that a randomly selected degree is in Engineering? Round to the nearest ten
thousandth, if necessary.
A) 0.1028
B) 868
C) 0.0932
1
D) 0.0012
6) Of the 81 people who answered "yes" to a question, 6 were male. Of the 70 people that answered "no" to the
question, 6 were male. If one person is selected at random from the group, what is the probability that the
person answered "yes" or was male?
A) 0.074
B) 0.576
C) 0.616
D) 0.079
Describe the complement of the given event.
7) When five athletes compete in the Olympics, at least one of them wins a medal.
A) When five athletes compete in the Olympics, no more than four of them win a medal.
B) When five athletes compete in the Olympics, none of them wins a medal.
C) When five athletes compete in the Olympics, all of them win a medal.
D) When four athletes compete in the Olympics, none of them wins a medal.
Find the indicated probability.
8) In a batch of 8,000 clock radios 4% are defective. A sample of 7 clock radios is randomly selected without
replacement from the 8,000 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?
A) 0.0400
B) 0.249
C) 0.751
D) 0.143
Identify the given random variable as being discrete or continuous.
9) The braking time of a car
A) Discrete
B) Continuous
Solve the problem.
10) Suppose you pay $3.00 to roll a fair die with the understanding that you will get back $5.00 for rolling a 1 or a
3, nothing otherwise. What is your expected value?
A) -$3.00
B) $3.00
C) $5.00
D) -$1.33
Find the indicated probability.
11) A company manufactures calculators in batches of 64 and there is a 4% rate of defects. Find the probability of
getting exactly three defects in a batch.
A) 0.139
B) 0.375
C) 0.221
2
D) 0.091
12) A machine has 11 identical components which function independently. The probability that a component will
fail is 0.2. The machine will stop working if more than three components fail. Find the probability that the
machine will be working.
A) 0.111
B) 0.162
C) 0.949
D) 0.839
13) A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a
standard deviation of 50. If an applicant is randomly selected, find the probability of a rating that is between
200 and 275.
A) 0.0668
B) 0.4332
C) 0.5
D) 0.9332
Solve the problem.
14) Suppose that replacement times for washing machines are normally distributed with a mean of 9.7 years and a
standard deviation of 1.1 years. Find the replacement time that separates the top 18% from the bottom 82%.
A) 9.9 years
B) 10.7 years
C) 8.7 years
D) 10.0 years
15) A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a
standard deviation of 50. If 40 different applicants are randomly selected, find the probability that their mean is
above 215.
A) 0.3821
C) 0.1179
B) 0.0287
3
D) 0.4713
Find the indicated probability.
16) The table below shows the soft drinks preferences of people in three age groups.
cola root beer lemon-lime
under 21 years of age 40
25
20
between 21 and 40 35
20
30
over 40 years of age 20
30
35
If one of the 255 subjects is randomly selected, find the probability that the person is over 40 and drinks cola.
4
4
A)
B)
17
19
C)
4
51
D) None of the above is correct.
17)
The table below describes the smoking habits of a group of asthma sufferers.
Light Heavy
Nonsmoker smoker smoker Total
Men
390
81
86
557
Women
384
83
64
531
Total
774
164
150 1088
If one of the 1088 subjects is randomly selected, find the probability that the person chosen is a nonsmoker
given that it is a woman. Round to the nearest thousandth.
A) 0.353
B) 0.723
C) 0.496
D) 0.388
C) 0.2239
D) -0.2237
If Z is a standard normal variable, find the probability.
18) The probability that Z lies between -1.10 and -0.36
A) 0.4951
B) 0.2237
4
Find the indicated probability.
19) The incomes of trainees at a local mill are normally distributed with a mean of $1100 and a standard deviation
$150. What percentage of trainees earn less than $900 a month?
A) 35.31%
B) 40.82%
C) 9.18%
D) 90.82%
Solve the problem.
20) The quadratic mean (or root mean square) is usually used in physical applications. In power distribution
systems, for example, voltages and currents are usually referred to in terms of their root mean square value.
The quadratic mean of a set of values is obtained by squaring each value, adding the results, dividing by the
number of values (n), and then taking the square root of that result, expressed as
quadratic mean =
∑x2
n
Find the root mean square of these power supplies (in volts): 63, 1, 91, 108.
A) 38.7 volts
B) 77.3 volts
C) 131.5 volts
D) 65.8 volts
21) Melissa is looking for the perfect man. She claims that of the men at her college, 32% are smart, 33% are funny,
and 16% are both smart and funny. If Melissa is right, what is the probability that a man chosen at random
from her college is neither funny nor smart?
A) 0.67
B) 0
C) 0.84
D) 0.51
E) 0.35
Use summary statistics to answer the question.
22) Here are some summary statistics for all of the runners in a local 12K race: slowest time = 140 minutes,
mean = 88 minutes, median = 88 minutes, range = 110 minutes, IQR = 59, Q1 = 35, standard deviation = 12
minutes. Between what two values are the middle 50% of times?
A) 140 and 30
B) 35 and 66
C) 35 and 94
5
D) 17.6 and 70.4
E) 35 and 88
Answer Key
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