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Statistics
1. A random sampling of 500 adults showed that 203 preferred Brand A potato chips more than all other
brands of potato chips in the survey. Which interval reflects a 95% likelihood of containing p, the
population proportion?
A.
B.
C.
D.
2. A university professor and his students did a study to determine the mean length of bass in a lake. Each
time a bass was caught, its length was measured in inches, and then it was released. The distribution of the
lengths is shown in the graph below.
Based on this graph, which measurement represents the best estimate for the mean length of bass in the
lake?
A. 11 inches
B. 17 inches
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C. 18 inches
D. 19 inches
3. An electronics company conducted a customer satisfaction survey. The
survey results showed, with a 95% confidence level, that 62% to 68% of
customers are satisfied with their service. What is the margin of error of
this survey?
A. 3%
B. 6%
C. 65%
D. 95%
4. A sociologist wants to determine a town’s population percentage willing to
make donations this year to help protect the nearby forest.
Approximately how many people does he need to survey in order to be
90% confident that the sample percentage is within a 3% margin of error
given that 42.5% of the people of the town are willing to donate?
A. 735
B. 1,339
C. 2,204
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D. 4,467
5. A survey of 640 people reports that 458 are willing to contribute to a
charity. What is the margin of error for this survey in order to
achieve a 95% confidence level in the estimate of the portion of
the population willing to contribute to a charity?
A. 0.009
B. 0.018
C. 0.035
D. 0.041
6. The results of a survey suggested that 64% of the voters will vote for a particular candidate in an election.
The candidate wants to be 95% confident that she will receive the majority of the votes in the election.
The results from 100 computer simulations of this situation are shown below.
Based on the margin of error and these simulations, what is the range of the percentages of votes this
candidate could receive?
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A. 0.43 to 0.63
B. 0.48 to 0.58
C. 0.54 to 0.74
D. 0.59 to 0.69
7. A group of high school students were asked about their favorite sports.
The survey indicated that 37% of students, or 407 students, said baseball
was their favorite sport.
Part A: What was the total number of students surveyed?
Part B: What is the margin of error of the survey for only the sample of
students who said baseball was their favorite sport?
Part C: Write an interval that is likely to contain the exact percentage of
all students who would say baseball is their favorite sport.
Use words, numbers, and/or pictures to show your work.
8. When 865 voters in a state are randomly selected and surveyed, it is
found that 70% of the voters support the current elected official. For a
95% confidence level, the margin of error for the population mean is
3.05%. Which statement explains how this survey could be adjusted so
that the population mean can be reported with a 99% confidence level?
A. If the margin of error is fixed at 3.05% and the sample size is
decreased to 500, the survey could be reported with a 99%
confidence level.
B. If the margin of error is fixed at 3.05% and the sample size is
increased to 1,200, the survey could be reported with a 99%
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confidence level.
C. If the sample size remains 865 and the margin of error is adjusted to
4.02%, this would result in a survey that could be reported with a
99% confidence level.
D. If the sample size remains 865 and the margin of error is adjusted to
2.08%, this would result in a survey that could be reported with a
99% confidence level.
9. The student government reported that 82% of 12th grade students prefer
a white rose for the senior class flower. The poll has a margin of error
of ±8%. Estimate the number of seniors who were polled.
A. 155
B. 125
C. 82
D. 13
10. In a random survey of 1,000 high school students, 65% said that math is
their favorite subject. Based on these survey results, which of these
represents a 95% confidence interval for the percentage of all high
school students who would choose math as their favorite subject?
A. 60% to 70%
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B. 62.04% to 67.96%
C. 62.5% to 67.5%
D. 63.52% to 66.48%
11. A sample of 250 students were asked for the average amount of money
they spend in a day. The data resulted in a mean of $5.50 with a
standard deviation of $2.45. If the mean amount of money that all
students spend in a day is between $5.10 and $5.90, approximately
which confidence level does the range represent?
A. 99%
B. 93%
C. 45%
D. 32%
Margin of Error
12.
Kyle is interested in finding out how many of the 1,143 students at his
school are right-handed or left-handed.
Part A. Kyle decides to survey a portion of the students at his school to
ask whether they are right-handed or left-handed. He carefully selects a
sample group, knowing that it should be random so that it is a good
representation of the whole school. For example, he would NOT want to
single out first basemen on the baseball team because first basemen are
more likely than the general population to be left-handed.
He conducts the survey on his sample group and compiles the results in
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a table. Finish filling in the table.
Part B. How many students did Kyle survey in all? What percentage of
the boys in Kyle’s sample are right-handed? What percentage of the girls
are right-handed? What percentage of all the students surveyed are
right-handed?
Total in sample:
Percentage of boys who are right-handed:
Percentage of girls who are right-handed:
Percentage of all students surveyed who are right-handed:
Part C. If Kyle’s sample group is representative, about how many
students in the whole school would be right-handed? Left-handed? Show
your work.
Part D. Kyle wants to get an idea of how accurate these results are, so
he will calculate the margin of error. He will take the percentage of righthanded students in his survey and determine the range around that
percentage in which the true percentage probably lies. He wants to have
a confidence level of 95%, which means there is a 95% chance that the
true value will be within that range.
For the margin of error formula, he will need the value of alpha
is equal to 1 minus the confidence level, or
which
He also needs the z-score corresponding to a confidence level of 95%. A
table shows that this z-score,
is 1.96.
The other piece of information he needs is the sample size, n, which is
226.
Substitute these numbers into the formula to find the margin of error, E,
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for Kyle’s sample.
Part E. Suppose you wanted to know the percentage of right-handed
people in the whole population of the United States. You want to take a
survey that will give meaningful results with a small margin of error, but
the bigger the sample, the more costly and time-consuming the survey
becomes.
The graph below shows the margin of error as a function of the sample
size, with the sample size n on the x-axis and the margin of error as a
percentage on the y-axis. Keeping in mind the fact that it can be
expensive and time-consuming to conduct a survey but you still want a
small margin of error, what sample size would you recommend? Explain
your answer.
13. A survey was conducted where 150 high school students were asked the
average amount of time they spent doing household chores in one week.
The data collected resulted in a mean time of 180.5 minutes with a
standard deviation of 5.5 minutes. Which of these represents a 95%
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confidence interval for the mean weekly hours spent doing household
chores of all high school students?
A. 171.5–189.5
B. 175–186
C. 178.25–182.75
D. 179.62–181.38
14. A state senator requested a survey of registered voters to determine public opinion of a new law. Of the
940 voters who responded to the survey, 61.7% were in favor of the new law, 35.1% were opposed, and
the rest were undecided. What is the margin of error of this survey with a 95% level of confidence?
A.
B.
C.
D.
15. Rebecca wants to estimate the average age of a penny that is in circulation. She randomly selects 100
pennies from a jar full of pennies and records their ages in years. The graph below shows the data she
collected.
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In order to estimate the average age of a penny in circulation, Rebecca uses an advanced statistical
technique to simulate the process of selecting 100 pennies and recording the ages. The graph below shows
the result of her simulations.
Based on her work, which of the following is the best estimate for the margin of error that Rebecca should
use when she comes up with her estimate with 95% confidence for the mean age of a penny in
circulation?
A. 2
B. 6
C. 12.5
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D. 14.5
16. A random sample of shoppers chose between two similar products, and 60% chose Brand A. Based on the
sample, 20 simulations were conducted, and the mean number of shoppers out of 100 that chose Brand A
are shown below.
Mean Frequency
55
1
57
1
58
2
59
5
60
4
61
3
62
3
63
1
Based on the simulations, which of the following is the most likely margin of error for the sample?
A.
B.
C.
D.
17. Assume that a computer or calculator is used to generate the confidence interval
the value of the margin of error E, if
A.
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What is
sample mean and E= margin of error?
B. 10.9
C. 13.6
D. 59.6
18. In a recent survey, 75% of people who were polled said that they prefer Brand A batteries to Brand B
batteries. In order to create a 95% confidence interval for the true proportion of people who prefer Brand
A batteries, a computer simulation was run 200 times. The results are shown on the graph below.
Based on the simulations, which value is the best estimate for the margin of error?
A. 0.10
B. 0.25
C. 0.75
D. 0.88
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19. A sample of 121 high school seniors were surveyed on their level of school spirit on a scale of 0–100. The
sample mean of this survey is 86. The known population standard deviation is 14 for all seniors in the
class. Which of these is a 95% confidence interval for the population mean?
A.
B.
C.
D.
20. Alfredo used a computer to generate the given interval limits
where
What is the value of if
sample mean and E = margin of error?
A. 49.6
B. 60.5
C. 62.2
D. 74.8
21. An art student learned how to make a paper frog using a paper folding technique. The student “hopped”
the frog 100 times. The distances of the “hops” in centimeters are recorded in the graph below.
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Based on the graph, which value is the best estimate of the mean?
A. 2.75
B. 7.25
C. 7.5
D. 7.75
22. A sports-and-exercise shop sampled its customer base one weekend and
asked 35 customers their age:
24, 24, 24, 24, 24, 24,
25, 25,
26, 26, 26, 26, 26, 26, 26, 26,
27, 27, 27,
28, 28, 28, 28, 28,
29, 29,
30, 30,
31,
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33, 33, 33,
36,
45,
46
Which interval estimate of the population mean has a margin of error of
1.7 ?
A.
B.
C.
D.
23. The life span of a light bulb is the amount of time the bulb will work in a
standard appliance before burning out. The life span of a set of 10,000
electric light bulbs is normally distributed. The mean life span is 300
days and the standard deviation is 40 days. The life spans of the light
bulbs follow a normal distribution curve like the one shown in the
diagram below.
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Which conclusion is correct?
A. There are fewer light bulbs with a life span between 420 days and
460 days than in any other interval.
B. There are fewer light bulbs with a life span between 180 days and
220 days than in any other interval.
C. There are more light bulbs with a life span between 220 days and
300 days than all the other light bulbs combined.
D. There are more light bulbs with a life span between 260 days and
380 days than all the other light bulbs combined.
24. In a college math class, 500 students took a final exam. The final exam
results showed students had an average score of 65.3% with a standard
deviation of 5.2%. The scores on the final exam followed a normal
distribution curve with population percentages as shown below.
How many students scored above 54.9% but below 70.5%?
A. 78
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B. 82
C. 341
D. 409
25. A general health study survey was conducted using 142 randomly selected students from several middle
schools. Each student’s resting pulse rate, recorded in beats per minute, was measured. The frequency
table shows the data from this survey are normally distributed.
Based on the data in the table, which percentage is the best estimate for the proportion of students that
have a resting pulse rate of at least 88 beats per minute?
A. 16.2%
B. 23.0%
C. 37.3%
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D. 53.0%
26. The ages of the employees of a company are normally distributed, with
the mean age being 32 years and a standard deviation of 2 years. Which
percentage of the employees are likely to be more than 33 years old?
A. 15.9%
B. 19.1%
C. 30.9%
D. 69.1%
27. The mean score of the students in Dr. Battle’s math class on the most recent quiz was 78 points with a
standard deviation of 6 points. If these scores can be modeled using a normal distribution, which
percentage best represents the number of students with quiz scores between 72 and 90 points?
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Approximate Percentages of Data in a Normal Distribution:
• 68% of the data lie within 1 standard deviation of the mean.
• 95% of the data lie within 2 standard deviations of the mean.
• 99.7% of the data lie within 3 standard deviations of the mean.
A. 68.0%
B. 81.5%
C. 95.0%
D. 97.5%
28. A large random sample was taken of body temperatures of women at a university. The data from the
sample were normally distributed with a mean body temperature of 98.52°F and a standard deviation of
0.727°F. Based on this sample, which percentage is the best estimate of the proportion of all women at
this university who have a body temperature more than 2 standard deviations above the mean?
A. 0.30%
B. 2.28%
C. 72.70%
D. 97.72%
29. The heights of the students in a class are normally distributed, with a
mean height of 62 inches and a standard deviation of 1.2 inches. Which
percentage of the students in the class are likely to have a height
between 61.4 and 62.6 inches?
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A. 19.10%
B. 34.10%
C. 38.2%
D. 69.10%
30. A book editor was proofreading a draft of a novel. She found that the
number of errors on each page of the book was normally distributed,
with the mean number of errors on a page as 8 and a standard deviation
of 1. If 82 pages had between 7 and 9 errors, what was the approximate
total number of pages in the book?
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A. 56 pages
B. 68 pages
C. 120 pages
D. 202 pages
31. Petra measures how long a particular brand of holiday light bulb remains
lit continuously before burning out. She samples 250 bulbs, and her data
forms a normal distribution, with a mean of 100 hours and a standard
deviation of 5 hours. What percent of the bulbs burned out between 105
and 110 hours?
A. 5.0
B. 10.3
C. 13.5
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D. 34.0
32. Jim works in the quality department at a bolt factory. He noted that a
particular batch of 120 bolts has a mean length of 20 centimeters (cm)
with a standard deviation of 2 cm. The number of bolts at particular
lengths fit a normal distribution curve.




What is the approximate number of bolts that have lengths that are
within one standard deviation of the mean?
What is the approximate number of bolts that have lengths that would
fall within one and two standard deviations away from the mean?
What is the approximate number of bolts that have lengths less than
16 cm?
While checking another batch, Jim randomly selected 10 bolts. Their
lengths were as follows: 5 cm, 9 cm, 17.5 cm, 18 cm, 18 cm, 18.5
cm, 18.5 cm, 19 cm, 21 cm, and 27 cm. The mean length of these
bolts is 17.15 cm, and the standard deviation is 5.78. Would it be
appropriate to fit the data set to a normal distribution? Why or why
not?
Use words, numbers, and/or pictures to show your work.
33. Use the table below to answer the following question.
Approximate Percentages of Data in a Normal Distribution:
• 68% of the data lie within 1 standard deviation of the mean.
• 95% of the data lie within 2 standard deviations of the mean.
• 99.7% of the data lie within 3 standard deviations of the mean.
The mean of the monthly utility bills in a town is $183.00, with a standard deviation of $17.00. Based on
the normal distribution, which value best represents the percentage of utility bills between $166.00 and
$217.00?
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A. 47.5%
B. 68.0%
C. 81.5%
D. 95.0%
34. Researchers at a computer company conducted a survey on the number of hours computers are being used
in households each day. The data from a random sample of 2,100 homes produced a normal distribution
with a mean length of time of 5.3 hours per day with a standard deviation of 0.9 hour. Based on the
sample, which percentage best represents the percentage of all households that use a computer less than 5
hours or more than 6 hours per day?
A. 21.8%
B. 36.9%
C. 41.2%
D. 58.7%
35. The graph shows a normal distribution with a standard deviation of 10.
Which percentage is the best estimate for the shaded area under this normal curve?
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A. 42.0%
B. 77.5%
C. 79.0%
D. 83.5%
36. The distributions below represent the batting averages of the players on
two baseball teams, A and B.
Which of these is true based on the graph?
I. The mean batting average for team A is less than the mean batting
average for team B.
II. The standard deviation for team A is less than the standard deviation
for team B.
A. I only
B. II only
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C. both I and II
D. neither I nor II
37. The cholesterol level for adults of a specific group is normally distributed
with a mean of 158.3 and a standard deviation of 6.2. The cholesterol
levels follow a normal distribution curve like the one shown in the
diagram below.
Which percent is closest to the group that has cholesterol below 152.1?
A. 13.5%
B. 16%
C. 81.5%
D. 84%
38. A factory manufactures bolts and packs them in boxes, with each
box containing 120 bolts. The lengths of the bolts in each box are
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normally distributed, having a mean length of 22 cm and a standard
deviation of 1 cm. About how many bolts having a length greater than 23
cm can be found in each box?
A. 16
B. 19
C. 34
D. 41
39. A local peach orchard packages 200 peaches per box. The weights of the
peaches are normally distributed with a mean of 5.5 ounces and a
standard deviation of 0.75 ounce. Approximately how many of the
peaches in each box weigh between 4.75 ounces and 6.25 ounces?
A. 34
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B. 68
C. 95
D. 136
40. A factory manufactures light bulbs and then packs them in boxes to be
shipped to its customers. Before each shipment, boxes are randomly
chosen and the bulbs inside are inspected. The number of bulbs found to
be defective in each box can be normally distributed. The mean number
of defective bulbs in each box is 12 with a standard deviation of 2.
Use the normal curve shown above to answer the questions. Let
represent the mean and represent the standard deviation.
Part A. If any one box among the sample of inspected boxes chosen has
a total of 9 defective bulbs, what percentage of the sample boxes will
have more defective bulbs than this box? Explain what this means in
terms of the given context.
Part B. If there are 60 boxes that contain between 12 and 15 defective
bulbs, how many total boxes were inspected?
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Use words, numbers, and/or pictures to show your work.
41. A random sample of 250 AM radio stations was taken. The dot plot displays the data collected. Each dot
represents the frequency in kilohertz (kHz) on which each station broadcasts.
Which statement best describes why using the mean and the standard deviation from this sample
would not be an appropriate way to estimate the proportion of all AM radio stations that broadcast
between 800 kilohertz and 1,000 kilohertz?
A. The distribution of the sample is not symmetrical.
B. The standard deviation of the sample will be larger than the mean.
C. A sample size of 250 is not large enough to estimate a population proportion.
D. The sample does not include enough radio stations broadcasting between 700 kilohertz and 900
kilohertz.
42. The selling prices of houses in a city during one year were normally distributed with a mean of $259,000
and a standard deviation of $15,000. Which of the following is closest to the percentage of these homes
that had a selling price between $244,000 and $289,000?
A. 47.7%
B. 68.2%
C. 81.8%
D. 95.4%
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43. A random sample of 108 customers was taken in a shopping mall. The mean number of purchases for this
sample of customers was 3.9 with a standard deviation of 1. The median was 4.4, and the mode was 4. A
graph shows that the distribution of the data is highly skewed to the left. A store manager wants to
calculate the probability that a customer will purchase at least 4 items. Which statement is true?
A. The probability can be accurately determined using the mean, standard deviation, and z-score table.
B. The probability can be accurately determined using the mode, standard deviation, and z-score table.
C. The probability can be accurately determined using the median, standard deviation, and z-score
table.
D. The probability cannot be accurately determined using the mean, standard deviation, or z-score
table.
44. In a normal distribution, 68% of all data points should fall within one
standard deviation of the mean.
A group of 1,200 students took an aptitude test. Their scores followed a
normal distribution. The mean score was 490, and exactly 600 students
scored between 424 and 556. Which value could be the standard
deviation for the distribution?
A. 50
B. 66
C. 90
D. 100
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45. Which data set is least likely to resemble a normal distribution?
A. the heights of all 14-year-old girls who live outside the state of Texas
B. the heights of all 14-year-old girls who go to school in the state of Texas
C. the heights of all 14-year-old girls who go to school in the city of Houston
D. the heights of all 14-year-old girls who live on a given street in the city of Houston
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