The
following problems are currently ( Fall 2003 ) not
covered on the Math 210 Final :
#34, 42,
51
This is in no way all of the information
that you should know for the FINAL.
FINAL REVIEW PROBLEMS
(1) According to the above histogram on the
heights of active volcanoes, how many volcanoes are less than 3500 feet tall?
(a) 5
(b) 8
(c) 10
(d) 12
(e) 15
(2) What is the missing frequency in the
following frequency distribution?
Class 
Frequency 
Cumulative Frequency 
09 
5 
5 
1019 
12 
17 
2029 
? 
32 
3039 
8 
40 
(a) 15
(b) 17
(c) 20
(d) 25
(e) 32
(3) For the data 5, 9, 2, 11, 7, 19, and 8,
what is the range?
(a) 3
(b) 7
(c) 11
(d) 17
(e) 19
(4) What is the mode of the following data
set: 2, 1, 3, 2, 1, 0, 4, 3, 2, 3, 4, 2, 1, 3, 2?
(a) 0
(b) 1
(c) 2
(d) 3
(e) 4
(5) A distribution has a mean of 200 and a
standard deviation of 30. For a data value of 245, what is the zscore?
(a) 1.50
(b) 1.20
(c) 1.20
(d) 1.50
(e) 1.75
(6) The value with 25% of the data
observations below it is the
(a) median
(b) first quartile (Q_{1})
(c) third quartile (Q_{3})
(d) mode
(e) interquartile range
(7) Find the sample variance of the following
data: 60, 72, 85, 89, 92, 54, 75, 81, 97.
(a) 13.66
(b) 14.49
(c) 17
(d) 186.67
(e) 210.00
(8) A teenager has 8 tee shirts, 2 belts, and
5 pairs of jeans. How many different outfits can he wear, assuming he always
wears a belt?
(a) 15
(b) 16
(c) 21
(d) 40
(e) 80
(9) A florist can select 5 different flowers
for a bouquet from a selection of 12 different types. How many different sets
of flowers can be chosen for the bouquet?
(a) 17
(b) 60
(c) 120
(d) 792
(e) 95040
(10) A photographer wishes to choose 4 photos
from a selection of 8 photos to display in a row on a wall. How many different
arrangements of photos can he choose from?
(a) 4
(b) 8
(c) 32
(d) 70
(e) 1680
(11) A box contains 5 red, 2 white, and 3
green marbles. If a marble is selected from the box at random, find the
probability that it is red or white.
(a) 0.2
(b) 0.3
(c) 0.5
(d) 0.7
(e) 0.8
(12) The probability of a
(a) 0.81
(b) 0.05
(c) 0.16
(d) 0.10
(e) 0.53
USE THE FOLLOWING INFORMATION TO ANSWER
QUESTIONS 13 & 14.
A store sells 3 types of appliances in 3 colors. The following table lists the
number of items of each type in stock.

White 
Almond 
Black 
Refrigerator 
12 
10 
3 
Washer 
10 
8 
5 
Dryer 
11 
11 
4 
(13) If an item is selected at random, what
is the probability that it is not black?
(a) 6/37
(b) 31/37
(c) 33/74
(d) 29/74
(e) 25/74
(14) Given that an appliance is white, what
is the probability that it is a refrigerator?
(a) 12/33
(b) 12/25
(c) 6/37
(d) 33/74
(e) 25/74
USE THE FOLLOWING INFORMATION TO ANSWER
QUESTIONS 15, 16, & 17
The probability distribution of the number of cartoons
watched by first graders on Saturday mornings is shown in the following table.
x 
0 
1 
2 
3 
4 
5 
P(x) 
0.2 
0.2 
0.3 
0.15 
0.1 
0.05 
(15) What is the mean of this distribution?
(a) 1.9
(b) 2.0
(c) 2.4
(d) 2.6
(e) 3.1
(16) What is the standard deviation of this
distribution?
(a) 0.34
(b) 1.41
(c) 1.99
(d) 2.37
(e) 5.6
(17) What is the probability that a randomly
selected child watches fewer than 3 cartoons?
(a) 0.15
(b) 0.30
(c) 0.45
(d) 0.70
(e) 0.85
(18) If we have a binomial distribution with
n = 200 and p = 0.47, what is the variance of this distribution?
(a) 106
(b) 94
(c) 49.82
(d) 44.18
(e) 7.06
(19) If we have a binomial distribution with
n = 5 and p = 0.35, what is the P(X=2)?
(a) 0.0336
(b) 0.1225
(c) 0.3364
(d) 0.70
(e) 1.75
(20) If approximately 32% of adults cut their
sandwiches in half before eating them, find the probability that in a group of
9 adults, exactly 4 cut the sandwich in half before eating it.
(a) 0.0015
(b) 0.0034
(c) 0.0105
(d) 0.1921
(e) 0.2681
(21) Scores on a statewide proficiency test
are normally distributed with mean 68.2 and standard deviation 14.6. The state
would like to identify the 10% of students with the lowest scores for remedial
work. What is the cutoff score for students needing remedial work?
(a) .0398
(b) 1.28
(c) 64.55
(d) 71.85
(e) 49.51
(22) The average hourly wage of workers at a
fast food restaurant is $5.85 with standard deviation $0.35. Assume that the
distribution is normally distributed. If a worker at this restaurant is
selected at random, find the probability that the worker earns more than $6.50
per hour.
(a) 0.4686
(b) 0.0314
(c) 0.0322
(d) 0.9686
(e) 0.4678
(23) The average repair cost for automatic
washers is $73 with a standard deviation of $8. The costs are normally
distributed. If 9 washers are repaired find the probability that the mean of
the repair bills will be less than $69.50.
(a) 0.1700
(b) 0.3300
(c) 0.4049
(d) 0.0951
(e) 0.0001
(24) A medical re
(a) H_{0}: m_{1}
 m_{2} ³ 0 vs. H_{a}: m_{1}  m_{2 }< 0
(b) H_{0}: s _{1}^{2}/s _{2}^{2} £ 1 vs. H_{a}:
s _{1}^{2}/s _{2}^{2} > 1
(c) H_{0}: m_{1}
 m_{2} = 0 vs. H_{a}: m_{1}  m_{2 (}not =) 0
(d) H_{0}: s _{1}^{2}/s _{2}^{2} ³ 1 vs. H_{a}:
s _{1}^{2}/s _{2}^{2} < 1
(e) H_{0}: m_{1}
 m_{2} £ 0 vs. H_{a}: m_{1}  m_{2 }> 0
(25) In 1993, 3% of elementary schools did not
have computers. In a sample of 180 elementary schools, find the probability
that 6 or fewer did not have computers.
(a) 0.3156
(b) 0.5832
(c) 0.7031
(d) 0.5160
(e) 0.0001
(26) A sample of 36 job seekers took an
average of 5.9 months to find a new job. If the population standard deviation
is 0.8 months, find the 95% confidence interval for the mean.
(a) (5.64, 6.16)
(b) (5.68, 6.12)
(c) (5.86, 5.94)
(d) (5.56, 6.24)
(e) (5.48, 6.32)
(27) A tourism group wishes to estimate the
average cost of a lobster dinner for their city within $0.50 with 95%
confidence. It is known that the standard deviation of prices is $2.25. How
large of a sample size should the group take?
(a) 1
(b) 9
(c) 78
(d) 88
(e) 7780
(28) Find the appropriate critical value to
use in a 99% confidence interval for the mean when s is unknown and the sample size is 18?
(a) 2.58
(b) 2.88
(c) 2.90
(d) 1.96
(e) 1.65
(29) A survey of 80 families showed that 36
of them had at least two TV sets at home. Find the 90% confidence interval for
the proportion of families with at least two TV sets.
(a) (29.76, 42.24)
(b) (0.364, 0.536)
(c) (0.359, 0.541)
(d) (0.445, 0.455)
(e) (0.407, 0.493)
(30) A pharmaceutical company wishes to
market a new product to consumers over the age of 50. They plan to advertise on
a certain TV show if the average age of the viewer is over 50. What hypotheses
should the company test?
(a) H_{0}: m ³ 50 vs. H_{a}: m < 50
(b) H_{0}: m £ 50 vs. H_{a}: m > 50
(c) H_{0}: m=50 vs. H_{a}: m (not =) 50
(d) H_{0}: ³ 50 vs. H_{a}: < 50
(e) H_{0}: £ 50 vs. H_{a}: > 50
USE THE FOLLOWING MINITAB OUTPUT TO ANSWER QUESTIONS
#31 AND #32
Minitab was used to obtain a fitted line plot
that relates the number of years of experience and the current annual income
(in thousands) for a random sample of blue collar workers.
Regression
The regression
equation is y = 11.0 + 2.66 x
Predictor 
Coef 
StDev 
T 
P 
Constant 
11.031 
2.050 
5.38 
0.000 
x 
2.6563 
0.5870 
4.52 
0.000 
S = 3.321 RSq = 71.9% RSq(adj) = 68.4%
(31) If a randomly selected worker has 5
years of experience, what is his expected annual salary.
(a) 24300
(b) 18000
(c) 20000
(d) 21640
(e) 26960
(32) What is the coefficient of correlation
(r) for the data used in the regression problem.
(a) 0.827
(b) 0.719
(c) 0.848
(d) 0.719
(e) 0.848
(33) Minitab was used to conduct a test of
hypothesis. What is the Pvalue for this test?
ZTest
Test of mu = 14.000 vs mu not = 14.000
The assumed sigma = 3.00
Variable 
N 
Mean 
StDev 
SE Mean 
Z 
P 
C1 
30 
14.647 
2.726 
0.548 
1.18 

(a) 0.1190
(b) 0.2380
(c) 0.3643
(d) 0.3810
(e) 0.7620
(34) Minitab was used to conduct a test of
hypothesis. What is the Pvalue for this test?
TTest of the Mean
Test of mu = 10.000 vs mu < 10.000
Variable 
N 
Mean 
StDev 
SE Mean 
T 
P 
C1 
26 
8.718 
3.042 
0.585 
2.19 

(a) Pvalue = 0.0143
(b) Pvalue = 0.019
(c) Pvalue = 0.038
(d) Pvalue = 0.0143
(e) Pvalue = 0.0286
(35) Minitab was used to conduct a test of hypotheses for
two samples. Based on this partial Minitab output, what conclusion should be
reached for the test when using a 0.05 level of significance?
Two Sample TTest and Confidence
Interval
Two sample T for
C1 vs C2

N 
Mean 
StDev 
SE Mean 
C1 
27 
8.72 
3.04 
0.59 
C2 
27 
9.84 
2.86 
0.55 
95% CI for mu C1  mu C2: ( 2.73, 0.49)
TTest mu C1 = mu C2 (vs not =): T= P=0.17 DF=
(a) Reject Ho
(b) Do Not Reject Ho
(c) There is not enough information given in the problem to make a decision.
(36) A random sample of 81 students at a
local university showed that they work an average of 100 hours per month with a
population standard deviation of 27 hours. Compute a 95% confidence interval
for the mean of the population.
(a) (94.03 , 105.97)
(b) (94.12 , 105.88)
(c) (95.07 , 104.94)
(d) (95.01 , 104.99)
(e) (93.02 , 106.98)
(37) It is known that the variance of the
population equals 484. With a 0.90 probability, how large of a sample would
have to be taken to provide a sampling error of 3 or less?
(a) n=89
(b) n=146
(c) n=207
(d) n=70434
(e) n=99991
(38) A large corporation wants to determine
whether the average age of their employees is significantly more than 40. A
sample of 20 employees is selected. The average age in the sample was 45 years
with a sample standard deviation of 5 years. Assuming the distribution of the
population is normal, what is the value of the test statistic that would be
used to determine if the mean age of the employees is significantly more than
40 years?
(a) 4.47
(b) 0.22
(c) 0
(d) 0.22
(e) 4.47
(39) The manager of the quality control
department at MNM Corporation, a producer of various kinds of batteries, has
said that their "D" size batteries last more than 87 hours. A sample
of 36 batteries showed an average life of 88.5 hours. Assume from past
information that it is known that the standard deviation of the population is 9
hours. In order to support his claim, the manager conducts a test of hypothesis
and gets 1 for the value of the test statistic. What conclusion should the
manager make if he uses a 0.05 level of significance?
(a) Reject Ho
(b) Do Not Reject Ho
(c) There is not enough information given in the problem to make a decision.
(40) In the last presidential election, a
national survey company claimed that more than 50% of all registered voters
voted for the Democratic candidate. In a random sample of 400 registered
voters, 208 voted for the Democratic candidate. What is
the null and alternative hypotheses that would be used to determine if more
than 50% voted Democratic?
(a) Ho: p ³ .52 versus Ha: p < .52
(b) Ho: p = .52 versus Ha: p (not =) .52
(c) Ho: p = .50 versus Ha: p (not =) .50
(d) Ho: p £ .50 versus Ha: p > .50
(e) Ho: p ³ .50 versus Ha: p < .50
(41) An automobile dealer wants to see if
there is a relationship between monthly sales and the interest rate. A random sample
of 4 months was taken. The results of the sample are presented below. What is
the slope of the least squares regression line?
Interest Rate (in percent) X 
9.2 
7.6 
10.4 
5.3 
Monthly Sales Y 
22 
20 
10 
45 
(a) 1.39
(b) 6.25
(c) 6.25
(d) 1.39
(e) 75.1
(42) Two new processing methods are tested at
a factory. It is hypothesized that there is no difference in the variances of
the time needed to process products. A sample of 11 products using Process A show a variance of 4.5 minutes and a sample of 8 products
using process B show a variance of 5.2 minutes. Using a 0.05 level of
significance, we want to determine if there is a difference in the variances of
the two processes. If we use the test statistic F = 5.2/4.5 = 1.56 , what is the appropriate rejection region?
(a) Reject Ho if F > 3.14
(b) Reject Ho if F > 3.14 or F < 0.275
(c) Reject Ho if F > 4.76 or F < 0.253
(d) Reject Ho if F > 3.95 or F < 0.210
(e) Reject Ho if F > 3.51 or F < 0.238
(43) A study of corporate business costs was
conducted to determine if there was a difference between the average amount
spent on dinner by executives and the average amount spent on dinner by
managers. What is the value of the test statistic in this test of hypothesis?

Executives 
Managers 
Sample Mean 
25.50 
22.50 
Sample Standard Deviation 
4.75 
2.83 
Sample Size 
32 
35 
(a) 1.960
(b) 3.172
(c) 6.338
(d) 3.104
(e) 6.265
(44) In a wage discrimination case involving
male and female employees, independent samples of male and female employees
with 5 years or more experience provided the following hourly wage results. We
wish to conduct a test of hypothesis using a 0.05 level of significance in
order to determine if the average hourly wage of the male workers is exceeds
the average hourly wage of the female workers. What are the appropriate degrees
of freedom for this test?

Male 
Female 
Sample Mean 
$9.25 
$8.70 
Sample Standard Deviation 
$1.00 
$0.80 
Sample Size 
21 
19 
(a) 20
(b) 38
(c) 19
(d) 21
(e) 18
(45) Independent random samples selected from
two normal populations produced the following results.

Sample 1 
Sample 2 
Sample Mean 
5.4 
4.9 
Sample Standard Deviation 
3.4 
4.8 
Sample Size 
17 
12 
We wish to conduct a test of hypothesis to
determine if the population means of these two samples are different. Using a
0.05 level of significance, what is the appropriate critical region for this
test?
(a) Reject Ho if t > 1.960 or t < 1.960
(b) Reject Ho if t > 1.796 or t < 1.796
(c) Reject Ho if t > 2.052 or t < 2.052
(d) Reject Ho if t > 2.201 or t < 2.201
(e) Reject Ho if t > 2.228 or t < 2.228
(46) An urn contains 6 green balls, 5 white
balls, and 3 brown balls. A ball is selected, its colored noted, and then it is
replaced. When two balls are selected in this manner, what is the probability
that both balls are brown?
(a) 0.0306
(b) 0.0329
(c) 0.0459
(d) 0.0495
(e) 0.2143
(47) A box contains 9 red, 5 yellow, and 4
blue marbles. A marble is drawn, it is not replaced, and a second marble is
drawn. What is the probability that both of the marbles are yellow?
(a) 0.0617
(b) 0.0654
(c) 0.0772
(d) 0.0865
(e) 0.2778
(48) A recent study shows that babies who
weigh less than 5.5 pounds at birth have a 40% chance to develop high blood
pressure as adults. If 12 babies who weighed less than 5.5 pounds at birth are
selected at random, what is the probability that at most two of these babies
will develop high blood pressure as adults?
(a) 0.020
(b) 0.064
(c) 0.083
(d) 0.917
(e) 0.980
(49) A purchasing agent has placed a rush
order for a particular raw material with two different suppliers, A and B. If
neither order arrives in 4 days, the production process must be shut down until
at least one of the orders arrives. The probability that supplier A can deliver
the material in 4 days is 0.55 and the probability that supplier B can deliver
the material in 4 days is 0.35. Assuming that the suppliers are independent of
each other, what is the probability the production process is shut down in 4
days (both orders are late)?
(a) 0.1925
(b) 0.2000
(c) 0.2925
(d) 0.7075
(e) 0.8075
(50) A certain basketball player is fouled
and awarded two freethrows. The probability that this player makes the first
shot is 80%. If he makes the first shot, the probability that he makes the
second shot increases to 90%. What is the probability that this player makes
both freethrows?
(a) 0.64
(b) 0.72
(c) 0.85
(d) 0.89
(e) 0.98
(51) A medical re
(a) H_{0}: m_{1}
 m_{2} ³ 0 vs. H_{a}: m_{1}  m_{2 }< 0
(b) H_{0}: s _{1}^{2}/s _{2}^{2} £ 1 vs. H_{a}:
s _{1}^{2}/s _{2}^{2} > 1
(c) H_{0}: m_{1}
 m_{2} = 0 vs. H_{a}: m_{1}  m_{2 (}not =) 0
(d) H_{0}: s _{1}^{2}/s _{2}^{2} ³ 1 vs. H_{a}:
s _{1}^{2}/s _{2}^{2} < 1
(e) H_{0}: s _{1}^{2}/s _{2}^{2} = 1 vs. H_{a}:
s _{1}^{2}/s _{2}^{2} (not =) 1
ANSWERS
(1) D (2) A (3) D (4) C (5) D (6) B (7) E (8)
E (9) D (10) E
(11) D (12) E (13) B (14) A (15) A (16) B (17) D (18) C (19) C (20) D
(21) E (22) B (23) D (24) E (25) C (26) A (27) C (28) C (29) C (30) B
(31) A (32) E (33) B (34) B (35) B (36) B (37) B (38) E (39) B (40) D
(41) C (42) D (43) D (44) E (45) D (46) C (47) B (48) C (49) C (50) B (51) E
[UTM] [MATH] [FACULTY] [Dr. McCullough's Home Page]