Resources

Resources

Interpret confidence intervals for population means

A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before treatment,

22

subjects had a mean wake time of

104.0\,\text{min}

. After treatment, the

22

subjects had a mean wake time of

81.1\,\text{min}

and a standard deviation of

24.2\,\text{min}

. Assume that the

22

sample values appear to be from a normally distributed population and construct a

95\%

confidence interval estimate of the mean wake time for a population with drug treatments. What does the result suggest about the mean wake time of

104.0\,\text{min}

before the treatment? Does the drug appear to be effective?

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95\%

confidence interval estimate of the mean wake time for a population with the treatment.

\newline

\text{min} < \mu < \square\,\text{min}

\newline

(Round to one decimal place as needed.)

When Famke charges her phone, it gains

2

percentage points each minute. When Famke uses her phone, it loses

5

percentage points each minute.

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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

percentage points.

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How long did Famke use her phone and how long did she charge it?

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1

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(A) There is not enough information to determine the exact time Famke used and charged her phone.

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(B) The given information describes an impossible situation.

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(C) Famke used her phone for

10

minutes, and charged her phone for

20

\newline

(D) Famke used her phone for

20

minutes, and charged her phone for

10

Lifetimes of Wristwatches A random sample of the lifetimes of

25

inexpensive wristwatches has a standard deviation of

4.5

months. Assume the variable is normally distributed. Use the chi-square distribution table to find any chi-square values to three decimal places. Round your final answers to one decimal place.

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0

2

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1

2

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95

\% confidence intervals for the variance and standard deviation.

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\begin{array}{l} ◻ < \sigma^{2} < ◻,\ ◻ < \sigma < ◻ \end{array}

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Submit Assignment

Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean

42

minutes and standard deviation

21

minutes. A researcher observed

44

students who entered the library to study. Round all answers to

4

decimal places where possible.

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a. What is the distribution of

X

X \sim N

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b. What is the distribution of

\bar{x}

\bar{x} \sim N

\newline

c. What is the distribution of

\sum x

\sum x \sim N

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d. If one randomly selected student is timed, find the probability that this student's time will be between

44

21

1

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44

students, find the probability that their average time studying is between

44

21

1

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f. Find the probability that the randomly selected

44

students will have a total study time more than

21

6

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g. For part e) and f), is the assumption of normal necessary?

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21

7

of the total study time for groups of

44

students will be given a sticker that says ＂Great dedication＂. What is the least total time that a group can study and still receive a sticker? minutes

Car Survey In a survey of

2,000

people who owned a certain type of car,

400

said they would buy that type of car again. What percent of the people surveyed were satisfied with the car?

\%

of the people surveyed were satisfied with the car. (Type a whole number.) Help me solve this View an example gere help - Clear all Check answer Review Progress Question

1

12

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

\quad

? Round to the nearest article.

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

students in the high school and found a mean of

186

messages sent per day with a standard deviation of

99

messages. At the

95 \%

confidence level, find the margin of error for the mean, rounding to the nearest whole number. (Do not write

\pm

\newline

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

with a margin of error of

29

. Write a confidence interval for the true mean SAT score of the graduating high school seniors.

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 \%

. The margin of error for the survey was

3 \%

. Write a confidence interval for the percentage of the population that supports Candidate A.

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 \%

. The margin of error for the survey was

4 \%

. Write a confidence interval for the percentage of the population that supports Candidate A.

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

students in the high school and found a mean of

193

messages sent per day with a standard deviation of

68

messages. At the

95 \%

confidence level, find the margin of error for the mean, rounding to the nearest whole number. (Do not write

\pm

\newline

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

students in the high school and found a mean of

199

messages sent per day with a standard deviation of

68

messages. At the

95 \%

confidence level, find the margin of error for the mean, rounding to the nearest whole number. (Do not write

\pm

\newline

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

students in the high school and found a mean of

176

messages sent per day with a standard deviation of

77

messages. At the

95 \%

confidence level, find the margin of error for the mean, rounding to the nearest whole number. (Do not write

\pm

\newline

A study was commissioned to find the mean weight of the residents in certain town. The study examined a random sample of

62

residents and found the mean weight to be

189

pounds with a standard deviation of

26

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

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

students in the high school and found a mean of

160

messages sent per day with a standard deviation of

51

messages. At the

95 \%

confidence level, find the margin of error for the mean, rounding to the nearest whole number. (Do not write

\pm

\newline

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

\mathbf{2 1 2}

graduating seniors and found the mean score to be

489

with a standard deviation of

107

. Use the normal distribution/empirical rule to estimate a

95

\% confidence interval for the mean, rounding all values to the nearest tenth.

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

graduating seniors and found the mean score to be

502

with a standard deviation of

92

. Use the normal distribution/empirical rule to estimate a

95

\% confidence interval for the mean, rounding all values to the nearest tenth.

Derin is travelling abroad with a

\$0.50

calling card. The rate to call her boyfriend in Japan is

\$0.75

per minute. The rate to call her family in Turkey is

\$0.50

per minute. Derin wants to spend at least

30

minutes calling her family in Turkey. Which of the following systems of inequalities best represents the relationship between

x

, the number of minutes Derin calls Japan, and

y

, the number of minutes Derin calls Turkey?

15

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For Company A there is a

65\%

chance that no claim is made during the coming year. If one or more claims are made, the total claim amount is normally distributed with mean

10,000

and standard deviation

1,500

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For Company B there is a

75\%

chance that no claim is made during the coming year, If one or more claims are made, the total claim amount is normally distributed with mean

9,000

and standard deviation

2,000

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Assuming that the total claim amounts of the two companies are independent, what is the probability that, in the coming year, Company B's total claim amount will exceed Company A's total claim amount?

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Www-awu.aleks.com/alekscgi/X/Isl.exe/

10

7

8

3

jH-lQ-WKpxOg\_PLIKaCnhGTWihcIRHj|Xyp

6

5

9

6

6

5

7

4

0

9

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Rejecting unreasonable claims based on average statistics

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A weight-loss clinic advertised that last month its patients, on average, lost

7\text{lb}

. Assuming that average refers to the mean, which of the following claims must be true based on this information?

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Note: More than one statement could be true. If none of the statements are true, mark the appropriate box.

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Last month all of their patients lost at least

7\text{lb}

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Last month at least one of their patients lost

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12\text{lb}

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Last month, the number of their clients who lost less than

\newline

7\text{lb}

was equal to the number of their clients who lost

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7\text{lb}

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Two months ago at least one of their patients lost at least

\newline

7\text{lb}

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Last month some of their patients lost exactly

7\text{lb}

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None of the above statements are true.

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The payload of an aircraft is the sum of the weight of the people on board, their luggage, and the cargo carried by the aircraft. A particular commercial aircraft has a maximum payload of

35,000\,\text{kg}

and cargo weighing

7,000\,\text{kg}

P

represents the number of people on board, and the weight of each person plus his or her luggage is assumed to be

100\,\text{kg}

, which of the following inequalities best represents the situation?

n a New York Times poll measuring a candidate's popularity, the newspaper claimed hat in

19

20

cases its poll results should be no more than three percentage points off in either direction. What confidence level are the pollsters working with, and what size sample should they have obtained?

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3 \%, 20

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6 \%, 20

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6 \%, 100

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95 \%, 33

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95 \%, 1068

Ray is buying some ginger roots to brew some fresh ginger ale. The price of the ginger roots is

\newline

G

, and Ray has a coupon for

10\%

\newline

0.9G

represents the price Ray pays for the ginger roots after using the coupon.

\newline

0.9

represent in this context?

\newline

1

\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

Linn wanted to determine how much of a difference it makes to use a certain product to treat the water she used to irrigate her corn crops. She used a randomized block design experiment to select parts of her land to irrigate with untreated lake water and others to irrigate with treated water. Then she measured the heights of the plants in those areas. Here are summary statistics for her experiment:

\newline

Average plant height per section

\newline

\newline

\newline

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\bar{x}_{L}=276\text{cm}

\newline

\bar{x}_{T}=337\text{cm}

\newline

Sample standard deviation

\newline

s_{L}=22\text{cm}

\newline

s_{T}=35\text{cm}

\newline

\newline

n_{L}=4

\newline

n_{T}=4

\newline

Linn wants to estimate the difference in the mean height (in centimeters) of the plants irrigated with each type of water (treated - lake). Assume that the conditions for inference have been met.

\newline

Which of the following is an appropriate confidence interval for

\newline

\mu_{T}-\mu_{L}

\newline

\newline

4

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0

ixl.com/math/geometry/exterior-angles-of-polygons?signInRedirect=https%

3

2

2

2

2

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mymail.lausd.net bookmarks

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Saturday Academy...

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Learn with an example

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Watch a video (D)

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Ver en espa\u00f1ol

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The diagram shows a convex polygon.

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\text{＂ Time ＂}

\text{＂ elapsed ＂}

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What is the sum of the exterior angle measures, one at each vertex, of this polygon?

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0

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Not feeling ready yet? These can help:

A friend has an IRA with an APR of

6.25\%

. She started the IRA at age

20

\$50

per month. How much will her IRA contain when she retires at age

65

? Compare that amount to the total deposits made over the time period.

\newline

After retirement the IRA will contain

\$\square

\newline

\int

\newline

(Do not round until the final answer. Then round to the nearest cent as needed.)

\newline

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Get more help -

\newline

Compute the total and annual returns on the described investment.

\newline

Six years after buying

150

shares of XYZ stock for

\$70

per share, you sell the stock for

\$16,300

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The total return is

\square

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(Do not round until the final answer. Then round to one decimal place as needed.)

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View an example

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The average number of miles (in thousands) that a car's tire will function before needing replacement is

68

and the standard deviation is

16

45

randomly selected tires are tested. Round all answers to

4

decimal places where possible and assume a normal distribution.

\newline

a. What is the distribution of

X

X-N(68

\newline

16

\newline

\sigma^{s}

\newline

0^{8}

\newline

b. What is the distribution of

\bar{x}

\bar{x}-N(68

\newline

c. If a randomly selected individual tire is tested, find the probability that the number of miles (in thousands) before it will need replacement is between

67

4

70

4

\newline

45

tires tested, find the probability that the average miles (in thousands) before need of replacement is between

67

4

70

4

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e. For part d), is the assumption that the distribution is normal necessary? YesO No

At a local restaurant, the amount of time that customers have to wait for their food is normally distributed with a mean of

28

minutes and a standard deviation of

5

minutes. What is the probability that a randomly selected customer will have to wait less than

33

minutes, to the nearest thousandth?

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Quarter Standards (Grade Repair) Assignment

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11.00

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Normal Distribution - Find Area

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Normal Distribution w/ Population

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1

20

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Statistics Calculator

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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

minutes and a standard deviation of

3

minutes. Out of the

283

days that Mason commutes to work per year, how many times would his commute be longer than

41

minutes, to the nearest whole number?

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Statistics Calculator

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Quarter Standards (rade Repair) Assignment

\newline

11

00

\newline

al Distribution - Find Area

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al Distribution w/ Population

\newline

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1

20

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Statistics Calculator

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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

minutes and a standard deviation of

3

minutes. Out of the

283

days that Mason commutes to work per year, how many times would his commute be longer than

41

minutes, to the nearest whole number?

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Statictics Calculator

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3

15

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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

and standard deviation

0

6

meters. The error made by the more accurate instrument is normally distributed with mean

0

and standard deviation

0

4

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Assuming the two measurements are independent random variables, what is the probability that their average value is within

0

5

meters of the height of the tower?

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You should determine the form of the probability by hand, but then you can use Python to compute the numerical value.

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\Sigma

be an alphabet. We can then think of a function

f: \wp\left(\Sigma^{\star}\right) \rightarrow \wp\left(\Sigma^{\star}\right)

as a function that takes a language over

\Sigma

as input and produces a language over

\Sigma

as output. (Think back to PS

6

's question about

\wp\left(\Sigma^{\star}\right)

if you're curious about why this is.)

\newline

Now, a new definition. A function

f: \wp\left(\Sigma^{\star}\right) \rightarrow \wp\left(\Sigma^{\star}\right)

is called monotone if the following is true:

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\forall A \in \wp\left(\Sigma^{\star}\right) . \forall B \in \wp\left(\Sigma^{\star}\right) .(A \subseteq B \rightarrow f(A) \subseteq f(B)) .

\newline

This definition is a bit more subtle than it might initially appear.

\newline

\Sigma=\{\mathrm{a}, \mathrm{b}\}

. Below is a list of four functions from

\wp\left(\Sigma^{\star}\right)

to itself. For each function, determine whether it's monotone. No justification is required.

\newline

1

f: \wp\left(\Sigma^{\star}\right) \rightarrow \wp\left(\Sigma^{\star}\right)

f(L)=L \cup\{

f: \wp\left(\Sigma^{\star}\right) \rightarrow \wp\left(\Sigma^{\star}\right)

0

\newline

2

f: \wp\left(\Sigma^{\star}\right) \rightarrow \wp\left(\Sigma^{\star}\right)

f: \wp\left(\Sigma^{\star}\right) \rightarrow \wp\left(\Sigma^{\star}\right)

2

f: \wp\left(\Sigma^{\star}\right) \rightarrow \wp\left(\Sigma^{\star}\right)

0

\newline

3

f: \wp\left(\Sigma^{\star}\right) \rightarrow \wp\left(\Sigma^{\star}\right)

f: \wp\left(\Sigma^{\star}\right) \rightarrow \wp\left(\Sigma^{\star}\right)

5

\newline

4

f: \wp\left(\Sigma^{\star}\right) \rightarrow \wp\left(\Sigma^{\star}\right)

f: \wp\left(\Sigma^{\star}\right) \rightarrow \wp\left(\Sigma^{\star}\right)

7

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

chaperones for a field trip with

24

\newline

Which of the following could be combinations of values for the students and the minimum number of chaperones the museum requires?

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2

\newline

72

\newline

Minimum number of chaperones:

9

\newline

16

\newline

Minimum number of chaperones:

2

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60

\newline

Minimum number of chaperones:

6

\newline

45

\newline

Minimum number of chaperones:

5

\newline

40

\newline

Minimum number of chaperones:

8

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The average production cost for major movies is

67

million dollars and the standard deviation is

23

million dollars. Assume the production cost distribution is normal. Suppose that

46

randomly selected major movies are researched. Answer the following questions. Give your answers in millions of dollars, not dollars. Round all answers to

4

decimal places where possible.

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a. What is the distribution of

X

X \sim N(67, 23^2)

\newline

b. What is the distribution of

\bar{x}

\bar{x} \sim N\left(67, \left(\frac{23}{\sqrt{46}}\right)^2\right)

\newline

c. For a single randomly selected movie, find the probability that this movie's production cost is between

69

73

million dollars.

23

0

\newline

d. For the group of

46

movies, find the probability that the average production cost is between

69

73

million dollars.

23

4

\newline

e. For part d), is the assumption of normal necessary?

23

5

23

6

The amount of pollutants that are found in waterways near large cities is normally distributed with mean

9.8\,\text{ppm}

and standard deviation

1.7\,\text{ppm}

35

randomly selected large cities are studied. Round all answers to

4

decimal places where possible.

\newline

a. What is the distribution of

X

X \sim N(9.8, 1.7^2)

\newline

b. What is the distribution of

\bar{x}

\bar{x} \sim N\left(9.8, \left(\frac{1.7}{\sqrt{35}}\right)^2\right)

\newline

c. What is the probability that one randomly selected city's waterway will have more than

9.8\,\text{ppm}

0.5

\newline

35

cities, find the probability that the average amount of pollutants is more than

9.8\,\text{ppm}

0.5

\newline

e. For part d), is the assumption that the distribution is normal necessary?

\newline

\newline

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f. Find the IQR for the average of

35

\newline

1.7\,\text{ppm}

4

1.7\,\text{ppm}

5

1.7\,\text{ppm}

6

1.7\,\text{ppm}

5

\newline

1.7\,\text{ppm}

5

Jelani needs to hire at least

12

artists for an upcoming event. He needs to hire visual artists, who will be paid

\$300

for the event, and performers, who will be paid

\$480

for the event. His budget for paying the artists is no more than

\$6,000

. He must hire at least

4

visual artists and at least

3

performers. Which of the following does not satisfy all of the conditions described?

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1

\newline

4

visual artists and

10

\newline

8

visual artists and

8

\newline

\$300

0

visual artists and

3

\newline

\$300

2

visual artists and

4

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

people who were waiting in line outside of Chef Domenica's bakery on a Tuesday, and

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?

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1

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(A) Sample size

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(B) Population size

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(C) Where the survey was given

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(D) The number of people who refused to respond

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

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

1

\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.

...