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Math Problems
Precalculus
Interpret confidence intervals for population means
The value of
x
x
x
is decreased by
86
%
86 \%
86%
. Which expression represents this situation?
\newline
0.86
x
0.86 x
0.86
x
\newline
0.14
x
0.14 x
0.14
x
\newline
x
−
0.86
x-0.86
x
−
0.86
\newline
1
−
0.86
x
1-0.86 x
1
−
0.86
x
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A spinner for a board-game is divided into four equal-sized sections colored red, green, yellow, and blue. If you land on a line between the colors, you keep spinning until you land on a color. Riley's turn is next. Which word or phrase describes the probability that she will land on red or yellow or green or blue?
\newline
unlikely
\newline
certain
\newline
likely
\newline
impossible
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Through ten games of basketball this season, Autumn has made
97
%
97 \%
97%
of her freethrows. Which word or phrase describes the probability that Autumn will hit her next free throw?
\newline
certain
\newline
an equal chance or
50
50
50
−
50
-50
−
50
\newline
impossible
\newline
likely
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A clinical trial was conducted to lest the eflectiveness of a drug for treating insomnia in obler subjocts. Before treatment,
20
20
20
subjects had a mean wake time of
101
101
101
.
0
0
0
min. After treatment, the
20
20
20
subjects had a mean wake time of
78.7
m
i
n
78.7 \mathrm{~min}
78.7
min
and a standard deviation of
23.2
m
i
n
23.2 \mathrm{~min}
23.2
min
. Assume that the
20
20
20
sample values appear to be from a normally distributed population and construct a
90
%
90 \%
90%
confidence interval estimate of the mean wake time for a population with drug treatments. What does the resull suggest about the mean wake time of
101
101
101
.
0
0
0
min before the treatment? Does the drug appear fo be effective?
\newline
Construct the
90
%
90 \%
90%
confidence interval estimate of the mean wake time for a population with the treatment.
\newline
□
min
<
μ
<
□
min
\square{\min }<\mu<\square \min
□
min
<
μ
<
□
min
\newline
(Round to one decimal place as neoded)
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A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjocts. Before treatment,
20
20
20
subjects had a mean wake time of
101
101
101
.
0
0
0
min. After treatment, the
20
20
20
suby mean wake tme of
78.7
m
i
n
78.7 \mathrm{~min}
78.7
min
and a standard deviation of
23.2
m
i
n
23.2 \mathrm{~min}
23.2
min
. Assume that the
20
20
20
sample values appear to be from a normally distributed population and construct a
90
%
90 \%
90%
confidence interval es mean wake time for a population with drug treatrents. What does the result suggest about the mean wake time of
101
101
101
.
0
0
0
min before the treatment? Does the drug appear to be eflective?
\newline
Construct the
90
%
90 \%
90%
confidence interval estimate of the mean wake time for a population with the treatment.
\newline
□
min
<
μ
<
□
min
\square \min <\mu<\square \min
□
min
<
μ
<
□
min
\newline
(Round to one docimal place as needed.)
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Using random sample data, an analyst estimated that in an upcoming election, a candidate will receive
45
%
45\%
45%
of the votes. The margin of error for this estimation is
4
%
4\%
4%
. Which of the following is the most appropriate conclusion based on the given estimate and margin of error?
\newline
Choose
1
1
1
answer:
\newline
(A) The candidate will receive exactly
45
%
45\%
45%
of the votes.
\newline
(B) The candidate will receive between
41
%
41\%
41%
and
45
%
45\%
45%
of the votes.
\newline
(C) The candidate will receive between
45
%
45\%
45%
and
49
%
49\%
49%
of the votes.
\newline
(D) The candidate will receive between
41
%
41\%
41%
and
49
%
49\%
49%
of the votes.
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When Famke charges her phone, it gains
2
2
2
percentage points each minute. When Famke uses her phone, it loses
5
5
5
percentage points each minute.
\newline
Once, Famke used her phone for some time, and then charged it for twice the amount of time she used it. In the end, her phone lost
10
10
10
percentage points.
\newline
How long did Famke use her phone and how long did she charge it?
\newline
Choose
1
1
1
answer:
\newline
(A) There is not enough information to determine the exact time Famke used and charged her phone.
\newline
(B) The given information describes an impossible situation.
\newline
(C) Famke used her phone for
10
10
10
minutes, and charged her phone for
20
20
20
minutes.
\newline
(D) Famke used her phone for
20
20
20
minutes, and charged her phone for
10
10
10
minutes.
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Articles in the American Sociology Review Year
\quad
Total number of articles
\quad
Percent that were quantitative The table summarizes the numbers of articles published in the American Sociology Review in two years. Quantitative articles use numerical data and statistics. How many more quantitative articles were published in the journal in
\quad
than in
\quad
? Round to the nearest article.
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A study of a local high school tried to determine the mean number of text messages that each student sent per day. The study surveyed a random sample of
149
149
149
students in the high school and found a mean of
186
186
186
messages sent per day with a standard deviation of
99
99
99
messages. At the
95
%
95 \%
95%
confidence level, find the margin of error for the mean, rounding to the nearest whole number. (Do not write
±
\pm
±
).
\newline
Answer:
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A study by the department of education of a certain state was trying to determine the mean SAT scores of the graduating high school seniors. The study found that the mean SAT score was
470
470
470
with a margin of error of
29
29
29
. Write a confidence interval for the true mean SAT score of the graduating high school seniors.
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A survey was given to a random sample of voters in the United States to ask about their preference for a presidential candidate. The percentage of people who said they preferred Candidate A was
64
%
64 \%
64%
. The margin of error for the survey was
3
%
3 \%
3%
. Write a confidence interval for the percentage of the population that supports Candidate A.
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A survey was given to a random sample of voters in the United States to ask about their preference for a presidential candidate. The percentage of people who said they preferred Candidate A was
80
%
80 \%
80%
. The margin of error for the survey was
4
%
4 \%
4%
. Write a confidence interval for the percentage of the population that supports Candidate A.
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A study of a local high school tried to determine the mean number of text messages that each student sent per day. The study surveyed a random sample of
95
95
95
students in the high school and found a mean of
193
193
193
messages sent per day with a standard deviation of
68
68
68
messages. At the
95
%
95 \%
95%
confidence level, find the margin of error for the mean, rounding to the nearest whole number. (Do not write
±
\pm
±
).
\newline
Answer:
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A study of a local high school tried to determine the mean number of text messages that each student sent per day. The study surveyed a random sample of
95
95
95
students in the high school and found a mean of
199
199
199
messages sent per day with a standard deviation of
68
68
68
messages. At the
95
%
95 \%
95%
confidence level, find the margin of error for the mean, rounding to the nearest whole number. (Do not write
±
\pm
±
).
\newline
Answer:
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A study of a local high school tried to determine the mean number of text messages that each student sent per day. The study surveyed a random sample of
61
61
61
students in the high school and found a mean of
176
176
176
messages sent per day with a standard deviation of
77
77
77
messages. At the
95
%
95 \%
95%
confidence level, find the margin of error for the mean, rounding to the nearest whole number. (Do not write
±
\pm
±
).
\newline
Answer:
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A study was commissioned to find the mean weight of the residents in certain town. The study examined a random sample of
62
62
62
residents and found the mean weight to be
189
189
189
pounds with a standard deviation of
26
26
26
pounds. At the
95
%
95 \%
95%
confidence level, use the normal distribution/empirical rule to estimate the margin of error for the mean, rounding to the nearest tenth. (Do not write
±
\pm
±
).
\newline
Answer:
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A study of a local high school tried to determine the mean number of text messages that each student sent per day. The study surveyed a random sample of
96
96
96
students in the high school and found a mean of
160
160
160
messages sent per day with a standard deviation of
51
51
51
messages. At the
95
%
95 \%
95%
confidence level, find the margin of error for the mean, rounding to the nearest whole number. (Do not write
±
\pm
±
).
\newline
Answer:
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A study by the department of education of a certain state was trying to determine the mean SAT scores of the graduating high school seniors. The study examined the scores of a random sample of
212
\mathbf{2 1 2}
212
graduating seniors and found the mean score to be
489
489
489
with a standard deviation of
107
107
107
. Use the normal distribution/empirical rule to estimate a
95
95
95
\% confidence interval for the mean, rounding all values to the nearest tenth.
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A study by the department of education of a certain state was trying to determine the mean SAT scores of the graduating high school seniors. The study examined the scores of a random sample of
129
129
129
graduating seniors and found the mean score to be
502
502
502
with a standard deviation of
92
92
92
. Use the normal distribution/empirical rule to estimate a
95
95
95
\% confidence interval for the mean, rounding all values to the nearest tenth.
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Derin is travelling abroad with a
$
0.50
\$0.50
$0.50
calling card. The rate to call her boyfriend in Japan is
$
0.75
\$0.75
$0.75
per minute. The rate to call her family in Turkey is
$
0.50
\$0.50
$0.50
per minute. Derin wants to spend at least
30
30
30
minutes calling her family in Turkey. Which of the following systems of inequalities best represents the relationship between
x
x
x
, the number of minutes Derin calls Japan, and
y
y
y
, the number of minutes Derin calls Turkey?
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Ray is buying some ginger roots to brew some fresh ginger ale. The price of the ginger roots is
\newline
G
G
G
, and Ray has a coupon for
10
%
10\%
10%
off.
\newline
The expression
0.9
G
0.9G
0.9
G
represents the price Ray pays for the ginger roots after using the coupon.
\newline
What does
0.9
0.9
0.9
represent in this context?
\newline
Choose
1
1
1
answer:
\newline
(A) The amount of the discount from the coupon
\newline
(B) The percent, as a decimal, of the discount from the coupon
\newline
(C) The percent, as a decimal, of the original price that Ray pays
\newline
(D) The amount Ray pays after using the coupon
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At a local restaurant, the amount of time that customers have to wait for their food is normally distributed with a mean of
28
28
28
minutes and a standard deviation of
5
5
5
minutes. What is the probability that a randomly selected customer will have to wait less than
33
33
33
minutes, to the nearest thousandth?
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When Mason commutes to work, the amount of time it takes him to arrive is normally distributed with a mean of
38
38
38
minutes and a standard deviation of
3
3
3
minutes. Out of the
283
283
283
days that Mason commutes to work per year, how many times would his commute be longer than
41
41
41
minutes, to the nearest whole number?
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Two instruments are used to measure the height of an bridge. The error made by the less accurate instrument is normally distributed with mean
0
0
0
and standard deviation
0
0
0
.
6
6
6
meters. The error made by the more accurate instrument is normally distributed with mean
0
0
0
and standard deviation
0
0
0
.
4
4
4
meters.
\newline
Assuming the two measurements are independent random variables, what is the probability that their average value is within
0
0
0
.
5
5
5
meters of the height of the tower?
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A museum requires a minimum number of chaperones proportional to the number of students on a field trip. The museum requires a minimum of
3
3
3
chaperones for a field trip with
24
24
24
students.
\newline
Which of the following could be combinations of values for the students and the minimum number of chaperones the museum requires?
\newline
Choose
2
2
2
answers:
\newline
A Students:
72
72
72
\newline
Minimum number of chaperones:
9
9
9
\newline
B Students:
16
16
16
\newline
Minimum number of chaperones:
2
2
2
\newline
C Students:
60
60
60
\newline
Minimum number of chaperones:
6
6
6
\newline
D Students:
45
45
45
\newline
Minimum number of chaperones:
5
5
5
\newline
E Students:
40
40
40
\newline
Minimum number of chaperones:
8
8
8
\newline
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Jelani needs to hire at least
12
12
12
artists for an upcoming event. He needs to hire visual artists, who will be paid
$
300
\$300
$300
for the event, and performers, who will be paid
$
480
\$480
$480
for the event. His budget for paying the artists is no more than
$
6
,
000
\$6,000
$6
,
000
. He must hire at least
4
4
4
visual artists and at least
3
3
3
performers. Which of the following does not satisfy all of the conditions described?
\newline
Choose
1
1
1
answer:
\newline
(A)
4
4
4
visual artists and
10
10
10
performers
\newline
(B)
8
8
8
visual artists and
8
8
8
performers
\newline
(C)
$
300
\$300
$300
0
0
0
visual artists and
3
3
3
performers
\newline
(D)
$
300
\$300
$300
2
2
2
visual artists and
4
4
4
performers
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A food reporter conducted a survey to determine whether people in a certain city like the new dessert created by Chef Domenica. The reporter asked
87
87
87
people who were waiting in line outside of Chef Domenica's bakery on a Tuesday, and
9
9
9
people refused to respond. Which of the following factors makes it least likely that a reliable conclusion can be drawn about whether people in the city like Chef Domenica's new dessert?
\newline
Choose
1
1
1
answer:
\newline
(A) Sample size
\newline
(B) Population size
\newline
(C) Where the survey was given
\newline
(D) The number of people who refused to respond
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The members of a city council wanted to know the opinions of all city residents about collaborating with local farms to set up a farmers market in the city square. The council surveyed a sample of
300
300
300
city residents who have purchased produce from local farms. The survey showed that the majority of those sampled were in favor of the farmers market. Which of the following is true about the city council's survey?
\newline
Choose
1
1
1
answer:
\newline
A It shows that the majority of city residents are in favor of the farmers market.
\newline
(B) The survey sample is biased because it is not representative of all city residents.
\newline
(c) The survey sample should have included farmers who live outside the city.
\newline
(D) The survey should have consisted entirely of farmers.
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