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Unformatted text preview: Part A: Multiple choice problems. Please answer these on the OMR sheet. Name: Date: 1. Which of the following is a quantitative variable?
A) The make of a TV
B) A person‘s gender
C) Fuel efﬁciency of a car
D) Whether a person is an university graduate or not
E) Whether a person has a charge account 2. The two types of quantitative variables are:
A) Ordinal and ratio
B) Interval and ordinal
C) Nominative and ordinal
D) Interval and ratio
E) Nominative and interval 3. If there are 130 values in a data set, how many classes should be created for a frequency histogram?
A) 4
B) 5
C) 6
D) 7
E) 8 4. If the random variable X has a mean of ,u and a standard deviation 0' , then (X  ,u )/ 0'
has a mean and standard deviation respectively:
A) p and 0' B) } ands
C) 1 and 0
D) 0 and 1 Use the following to answer questions 5—6: The fuel efﬁciency rating for a midsize car is normally distributed with a mean of 32 and a
standard deviation of .8. What is the probability that the rating for a selected midsize car would
be: Page 1 5. Less than 33.2?
A) 43.32%
B) 6.68% C) 93.32%
D) 86.64%
E) 13.36% . More than 33.2?
A) 43.32%
B) 6.68%
C) 93.32%
D) 86.64%
E) 13.36% Ch Use the following to answer questions 710: A CFO is looking at how much of a company‘s resources are spent on computing. The CFO
samples companies in the pharmaceutical industry and developed the following stemand—leaf 5 269 6 255568999 7 11224557789
8 001222458 9 02455679 10 1556 11 137 12 13 255 7. What is the approximate shape ofthe distribution of the data?
A) Normal
B) Skewed to the right
C) Skewed to the leﬁ
D) Bimodal
E) Uniform Page? 8. What is the smallest percent spent?
A) 5.9
B) 5.6
C) 5.2
D) 5.02
E) 50.2 9. If a frequency histogram were to he created using these data, how many classes would
' you create?
A) 4
B)
C)
D)
E) OO\IO\U‘I 10. What would be the class length that would be used in creating a frequency histogram?
A) 1.4
B) 8.3
C) 1.2
D) 1.7
E) 0.9 Use the following to answer questions 1113: The numbers of rooms for 15 homes recently sold were:
8, 8, 8, 5, 9, 8, 7, 6, 6, 7, 7, 7, 7, 9, 9 11. What is the mean?
A) 8.0
B) 7.0
C) 6.0
D) 9.0
E) 7.4 12. What is the median?
A) 8.0
B) 7.0
C) 6.0
D) 9.0
E) 7.4 Page 3 13. 14. 15. 16. 17. What is the mode?
A) 8.0
B) 7.0
C) 6.0
D) 9.0
E) 7.4 As the sample size the variation of the sampling distribution of X
Decreases, decreases
Increases, remains the same
Decreases, remains the same
Increases, decreases None of the above are correct A)
B)
C)
D)
E) Consider a sampling distribution formed based on n = 3. The standard deviation of the
population of all sample means a)? is less than the standard deviation of the population of individual measurements 0'.
A) Always B) Sometimes C) Never The mean life of pair of shoes is 40 months with a standard deviation of 8 months. If
the life of the shoes is normally distributed, how many pairs of shoes out of one million
Will need replacement before 36 months? A) 500,000 B) 808,500 C) 191,500 D) 308,500 B) 705,100 and standard deviation of A standard normal distribution has a mean of
A) zero, zero B) zero, one C) one, one D) one, zero E) none of the above are correct Page 4 18. 19. 20. 21. 22. The area under the standard normal curve between Z = O and z = l is the area under the normal curve between Z =1 and z = 2.
A)
B)
C)
D)
E) Less than Greater than Equal to A, B, or C above dependent on the value of the mean A, B, or C above dependent on the value of the standard deviation If the wages of workers for a given company are normally distributed with a mean of
$15 per hour, then the proportion of the workers earning more than $13 per hour: A) Is greater than the proportion earning less than $13 per hour. B) Is greater than the proportion earning less than $18 per hour. C) Is less than 50%. D) Is less than the proportion earning more than the mean wage. E) None of the above are correct A student's grade on an examination was transformed to a 2 value which is negative.
Therefore, we know that he scored: A) Higher than 16% of the class B) Higher than 45% of the class C) Above the ﬁrst quartile D) Lower than 16% of the class E) Below the mean The relationship between the standard normal random variable Z and normal random
variable X is that: A) Only the normal random variable X is continuous. B) Only the standard normal variable Z is continuous. C) The standard normal variable Z counts the number of standard deviations that the
value of the normal random variable X is away from its mean. The values of the standard normal random variable Z can not be negative. The values of the normal random variable X can not be negative. D)
E) The central limit theorem states that as the sample size increases the distribution of the
sample approach the normal distribution. A) medians B) modes C) standard deviations D) variances E) means  Page 5 23. Consider two population distributions labelled A and B. Distribution A is highly skewed
and nonnormal, while the distribution B is slightly skewed and near normal. In order
for the sampling distributions of A and B to achieve the same degree of normality: A) Population A will require a larger sample size. B) Population B will require a larger sample size. C) Population A and B will require the same sample size.
D) Both (B) and (C) are correct E) None of the above (A, B, or C) are correct 24. If the sampled population has a mean 48 and standard deviation 16, then the mean and the standard deviation for the sampling distribution of A7 for n = 16 are: A) 4andl B) 12and4
C) 48and4
D) 48andl
E) 48and16 25. If we have a sample size of 100 and the estimate of the population proportion is .10, the
standard deviation of the sampling distribution of the sample proportion is:
A) .0009
B) .03
C) 3
D) 9
E) .10 26. For nonnormal populations, as the sample size (n) , the
distribution of sample means approaches a(n) distribution.
A) Decreases, Uniform
B) Increases, Normal
C) Decreases, Normal
D) Increases, Uniform
E) Increases, Exponential Use the following to answer questions 2729: In a manufacturing process a machine produces bolts that have an average length of 3 cm with a
variance of .03. If we randomly select three bolts ﬁ'om this process: Page 6 27. 28. 29. 30. 31. What is the standard deviation of the sample mean?
A) .03 B) .01 C) .1732 D) .0577 E) .10 What is the probability the mean length of the bolts is at least 3.16 cm?
A) 97.72 % B) 5.48 % C) 94.52 % D) 44.52 % E) 2.28 % What is the probability the mean length of the bolts is at most 3.1 cm?
A) 84.13% B) 100 % C) 71.57 % D) 28.43 % E) 15.87 % Which percentile describes the ﬁrst quartile, Ql?
A) 25th B) 50th C) 75th D) 100th E) 125th Which of the following is inﬂuenced the least by the occurrence of extreme values in a
sample? A) Mean B) Median C) Mode D) Geometric mean E) Weighted mean Page 7 32. If there are 62 values in a data set, how many classes should be created for a frequency histogram?
A) 4
B) 5
C) 6
D) 7
E) 8 33. Ratio variables have the following unique characteristic:
A) meaningful order
B) an inherently deﬁned zero value
C) categorical in nature D) predictable
E) equal distance between points Use the following to answer questions 34—35: In a statistic class, 10 scores were randomly selected with the following results were obtained:
74, 73, 77, 77, 71, 68, 65, 77, 67, 66 34. What is the mean?
A) 71.5
B) 72.0
C) 77.0
D) 71.0
E) 73.0 35. What is the median?
A) 71.5
B) 72.0
C) 77.0
D) 71.0
E) 73.0 Use the following to answer questions 36—37: According to a survey of the top 10 employers in a major city, a worker spends an average of
413 minutes a day on the job. Suppose the standard deviation is 26.8 minutes and the time spent
is approximately a normal distribution. Page 8 36. What are the times that approximately 68.26% of all workers will fall?
A) [394.8 431.2]
B) [386.2 439.8]
C) [372.8 453.2]
D) [359.4 466.6]
B) [332.6 493.4] 37. What are the times that approximately 95.44% of all workers will fall?
A) [387.5 438.5]
B) [386.2 439.8]
C) [372.8 453.2]
D) [359.4 466.6]
B) [332.6 493.4] Use the following to answer questions 3840: A local airport keeps track of the percentage of ﬂights arriving within 15 minutes of their
scheduled arrivals. The stemandleaf plot of the data for one year is below: 76 9
77 114
78 79 O7
80 88
81 2
82 1
83 88 38. What is the sample size?
A) 7
B) 9
C) 10
D) 11
E) 12 Page 9 39. In developing a histogram of these data, how many classes would be used?
A) 4
B)
C)
D)
E) 00qu 40. What would be t 1e class length for creating h 6 frequency histogram?
A) 1.4
B) 0.8
C) 2.7
D) 1.7
E) 2.3 Page 10 Answer Key pWHQMwar NHr—tr—tr—Ar—Ahtv—tn—KHp—t
ppws99%wwe9 mwmwmmwmeNNNNNNNNN
PWSQM%WPEQPWHQM¥PNF
o>muww>wow>>wmwwo>mom>wwU>wam>oowmoumuo 4;
.0 Page 11 Part B: Short answer problems. Please answer these in the space provided at the end of the exam
paper. Name: Date: 1. The population of lengths of aluminum—coated steel sheets is normally distributed with a
mean of 30.05 cm and a standard deviation of 0.3 cm. What is the probability that
average length of steel sheets from a sample of 9 units is more than 29.95 cm long? 2. The time of travel from a person's apartment to the bus station follows a uniform
distribution over the interval ﬁom 20 to 30 minutes. If they leave home at 9:05 AM,
what is the probability that they will get to the station between 9:25 and 9:30 AM? Use the following to answer questions 34:
The chief chemist for a major oil/ gasoline production company claims that the regular unleaded
gasoline produced by the company contains on average 4 grams of a certain ingredient. The chemist further states that the distribution of this ingredient per L of regular unleaded gasoline is
normal and has a standard deviation of 1.2 grams. 3. What is the probability of ﬁnding an average in excess of 4.3 grams of this ingredient
from randomly inspected 100L of regular unleaded gasoline? 4. What is the probability of ﬁnding an average less than 3.85 grams of this ingredient
from randomly inspected 64L of regular unleaded gasoline? Use the following to answer question 5: Suppose that the times required for a cable company to fix cable problems in its customers'
homes are uniformly distributed between 40 minutes and 65 minutes. 5. What is the probability that a randomly selected cable repair visit will take at least 50
minutes? Page 1 Use the following to answer questions 67 : An insurance company will insure a $75,000 Hummer for its full value against theft at a
premium of $1500 per year. Suppose that the probability that the Hummer will be stolen is
0.0075. 6. Calculate the insurance company‘s expected net proﬁt. 7. Find the premium that the insurance company should charge if it wants its expected net
proﬁt to be $2000? Use the following to answer questions 89: In the upcoming students' council election, the most recent poll based on 900 students predicts
that the incumbent will be re—elected with 55% of the votes. 8. From the 900 students, how many indicated that they would not vote for the current
students' council president or indicated that they were undecided? 9. For the sake of argument, assume that 51% of the actual student voters in the university
support the incumbent council president (p = 0.51). Calculate the probability of
observing a sample proportion of voters 0.55 or higher supporting the incumbent
council president. 10. A machine is made up of 3 components: an upper part, a mid part, and a lower part.
The machine is then assembled. 5 percent of the upper parts are defective; 4 percent of
the mid parts are defective; 1 percent of the lower parts are defective. What is the
probability that a machine is nondefective? Use the following to answer questions 1112:
X has the following probability distribution P(X): X 1 2 3 4
P(x) .1 .5 .2 .2 Page 2 11. Compute the expected value of X. 12. Compute the variance value of X.
Use the following to answer questions 1314:
It is very common for a television series to draw a large audience for special events or or
cliff—hanging story lines. Suppose that on one of these occasions, the special show drew viewers from 38.2% of all TV—viewing households. Suppose that three TV—Viewing households are
randomly selected. 13. What is the probability that all three households Viewed this special show? 14. What is the probability that none of the three households viewed this special show?
Use the following to answer questions 15—17:
A survey is made in a neighbourhood of 80 voters. 65 were Liberal and 15 were Conservative
(none claimed to support another political party). Of the Liberals, 35 are women, while 5 of the Conservatives are women. If one subject from the group is randomly selected, ﬁnd the
probability: 15. The individual is either a woman or a Liberal.
16. A male Conservative
17. A Liberal or a Conservative. Use the following to answer question 18: A random sample of size 1,000 is taken from a population where p = .20. 18. Find P(f9 <.18). Page 3 19. 20. Three candidates run for different ofﬁces in different counties; Each has a one in three chance of being elected in his/her county. What is the probability that at least one of
them will be elected? Packages of sugar bags for Sweeter Sugar Inc. have an average weight of 16 grams and
a standard deviation of 0.2 grams. The weights of the sugar bags are normally
distributed. What is the probability that 16 randomly selected packages will have an
average weight in excess of 16.075 grams? Page 4 Answer Key 1. 0.8413 P Z >3995gﬂ§ =P(Z >—1)=.3413+.5 =.8413 J9
.5 25min.—20min._ 5 .[\.J 10min. 3. .0062
43—4 .3
Z— 12 —E—2.5 0100 Pa? > 4.3) =.5—.4938 = .0062
4..1587
3.85—4 —0.15
Z: =—=—1.0
1.2 0.15 m Po? < 3.85) =.5—.3413 =.1587
5. .60 p(x > 50) = 6. $937.50
11.: (73500)(.0075) + (1500)(.9925)=551.25+1488.75=937.50 7. $2,562.50
2000 = (x75000)(.0075) + x(.9925)=.0075x — 562.5 + .9925x=2562.5
8. 405 (.45)(900) = 405
9..0082 67p 2 ‘ =.0167
900 Z = 55—51
.0167
P( 13).55) = .5 —.4918 = .0082
10..9029 (.95)(.96)(.99) = .9029
11. 2.5 E[X] = (1)(.1) + (2)(.5) + (3)(.2) + (4)(.2) = 2.5
12..9125
E[X] = (1)(.1) + (2)(.5) + (3)(.2) + (4)(.2) = 2.5
62): = = (1 — 2.5) 2 (.1) + (2 — 2.5)2 (.5) + (3 — 2.5)2 (.2) + (4 — 2.5)2 (.2) = .9125 65—50_§_ — —.6
65 —40 25 = 2.4 Page 5 13..056
L382)Q382)Q382)=.05574
14..236
(618)Q618)0613ya236
15..875
P(WnD) = P(W) + P(D) — P(Wu D)
(40/80)4—(65/80)—(35/80)==.875 160.125
(uy80)=.125
17.:L00
18=.0571
Z=ﬂ=i=4581
L2)L8) .01265
1000
P(f) <.18) =.5—.4429 =..0571
19..7037 .HXZD=LJm¥=m 32 1 ° 2 3 8
P‘X=°)[éi][§] (3] =5 P(X21)=1—£=£=.7037 27 27
20. 0.0668 >16.075 —16
.2 058 P Z = P(Z > 1.5) = .5 —.4332 = .0668 Page 6 ...
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