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# (Solved) MATH225 WEEK 6 QUIZ

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QUESTION 1

A statistics professor recently graded final exams for students in her introductory statistics course. In a review of her grading, she found the mean scoreÂ out ofÂ 100Â points was aÂ xÂ¯=77, with a margin of error ofÂ 10.

Construct a confidence interval for the mean score (out ofÂ 100Â points) on the final exam.

QUESTION 2

A random sample of adults were asked whether they prefer reading an e-bookÂ over a printed book. The survey resulted in a sample proportion ofÂ pâ€²=0.14, with a sampling standard deviation ofÂ Ïƒpâ€²=0.02, who preferred reading an e-book.

Use the empirical rule to constructÂ aÂ 95%Â confidence interval for the true proportion of adults who prefer e-books.

QUESTION 3

The pages per book in a library are normally distributed with an unknown population mean. A random sample of books is taken and results in aÂ 95%Â confidence interval ofÂ (237,293)Â pages.

What is the correct interpretation of theÂ 95%Â confidence interval?

• We estimate withÂ 95%Â confidence that the sample mean is betweenÂ 237Â andÂ 293Â pages.
• We estimate thatÂ 95%Â of the time a book is selected, there will be betweenÂ 237Â andÂ 293Â pages.
• We estimate withÂ 95%Â confidence that the true population mean is betweenÂ 237Â andÂ 293Â pages.

QUESTION 4

The population standard deviation for the heights of dogs, in inches, in a city isÂ 3.7Â inches. If we want to beÂ 95%Â confident that the sample mean is withinÂ 2Â inches of the true population mean, what is the minimum sample size that can be taken?

Use the table above for theÂ z-score, and be sure to round up to the nearest integer.

QUESTION 5

Clarence wants to estimate the percentage of students who live more than three miles from the school. He wants to create aÂ 98%Â confidence interval which has an error bound of at mostÂ 4%. How many students should be polled to create the confidence interval?

 z0.10 z0.05 z0.025 z0.01 z0.005 1.282 1.645 1.960 2.326 2.576

Use the table of values above.

QUESTION 6

The average score of a random sample ofÂ 87Â senior business majors at a universityÂ who took a certain standardized testÂ follows a normal distributionÂ with a standard deviation ofÂ 28. Use Excel to determine aÂ 90%Â confidence interval for the mean of the population.Â Round your answers to two decimal places and use ascending order

QUESTION 7

A random sample ofÂ 28Â statistics tutorials was selected from the pastÂ 5Â years and the percentage of students absent from each one recorded. The results are given below. Assume the percentages of students’ absences are approximately normally distributed. Use Excel to estimate the mean percentage of absences per tutorial over the pastÂ 5Â years withÂ 90%Â confidence. Round your answers to two decimal places and use increasing order.

QUESTION 8

Eric is studying people’sÂ typing habits. He surveyedÂ 525Â people and asked whether they leave one space or two spaces after a period when typing.Â 440Â people responded that they leave one space. Create aÂ 90%Â confidence interval for the proportion of people who leave one space after a period.

• Round your results to four decimal places.

QUESTION 9

A sample ofÂ 27Â employees for the Department of Health and Human Services has the following salaries, in thousands of dollars. Assuming normality, use Excel to find theÂ 98%Â confidence interval for the true mean salary, in thousands of dollars. Round your answers to two decimal places and use increasing order.

QUESTION 10

The population standard deviation for the heights of dogs, in inches, in a city isÂ 3.7Â inches. If we want to beÂ 95%Â confident that the sample mean is withinÂ 1Â inch of the true population mean, what is the minimum sample size that can be taken?

z0.101.282z0.051.645z0.0251.960z0.012.326z0.0052.576

Use the table above for theÂ z-score, and be sure to round up to the nearest integer.

QUESTION 11

A random sample of house sizes in major city has a sample mean ofÂ xÂ¯=1204.9Â sq ft and sample standard deviation ofÂ s=124.6Â sq ft.Â  Use the Empirical Rule to determine the approximate percentage of house sizesÂ that lie betweenÂ 955.7Â andÂ 1454.1Â sq ft.

QUESTION 12

The graph below shows the graphs of several normal distributions, labeledÂ A,Â B, andÂ C, on the same axis. Determine which normal distribution has the smallest standard deviation.

QUESTION 13

The resistance of a strain gauge is normally distributed with a mean ofÂ 100Â ohms and a standard deviation ofÂ 0.3Â ohms. To meet the specification, the resistance must be within the rangeÂ 100Â±0.7Â ohms. What proportion of gauges is acceptable?

QUESTION 14

A baker knows that the daily demand for strawberry pies is a random variable that follows the normal distribution with a mean ofÂ 31.8Â pies and a standard deviation ofÂ 4.5Â pies. Find the demand that has anÂ 8%Â probability of being exceeded.

QUESTION 15

A group of friends has gotten very competitive with their board game nights. They have found that overall, they each have won an average ofÂ 18Â games, with a population standard deviation ofÂ 6Â games.Â If a sample of onlyÂ 2Â friends is selected at random from the group, select the expected meanÂ and the standard deviation of the sampling distribution from the options below. Remember to round to the nearest whole number.

Select all that apply:

• ÏƒxÂ¯=6Â games
• ÏƒxÂ¯=3Â games
• ÏƒxÂ¯=4Â games
• Î¼xÂ¯=18Â games
• Î¼xÂ¯=3 gameS
• Î¼xÂ¯=9Â games

QUESTION 16

An elementary school has a population ofÂ 635Â students,Â 600Â of whom have received the chicken pox vaccine. The school nurse wants to make sure that the school meets all state requirements for vaccinations at public schools.

Find the population proportion, as well as the mean and standard deviation of the sampling distribution for samples of sizeÂ n=120.

Round all answers to 3 decimal places.

QUESTION 17

The lengths of text messages are normally distributed with an unknown population mean. A random sample of text messages is taken and results in aÂ 95%Â  confidence interval ofÂ (23,47)Â characters.

What is the correct interpretation of theÂ 95%Â  confidence interval?

• We estimate thatÂ 95%Â of text messages have lengths betweenÂ 23Â andÂ 47Â characters.
• We estimate withÂ 95%Â confidence that the true population mean is betweenÂ 23Â andÂ 47Â characters.
• We estimate withÂ 95%Â confidence that the sample mean is betweenÂ 23Â andÂ 47Â characters.

QUESTION 18

Given the plot of normal distributionsÂ AÂ andÂ BÂ below, which of the following statements is true? Select all correct answers.

Select all that apply:

• AÂ has the larger mean.
• BÂ has the larger mean.
• The means ofÂ AÂ andÂ BÂ are equal
• AÂ has the larger standard deviation
• BÂ has the larger standard deviation.
• The standard deviations ofÂ AÂ andÂ BÂ are equal.

QUESTION 19

A tour guide company is trying to decide if it is going to increase the cost of its tours to cover its sunk costs. They find that the average sunk cost per tour isÂ \$58, with a standard deviation ofÂ \$18. If they take a random sample ofÂ 36Â tours, identify each of the following to help them make their decision and round to the nearest hundredth if necessary:

QUESTION 20

From a recent company survey, it is known that the proportion of employees older thanÂ 55Â and considering retirement isÂ 8%. For a random sample of sizeÂ 110, what is standard deviation for the sampling distribution of the sample proportions, rounded to three decimal places?

QUESTION 21

In order to estimate the average electricity usage per month, a sample ofÂ 125Â residential customers were selected, and the monthly electricity usage was determined using the customers’ meter readings. Assume a population variance ofÂ 12,100kWh2. Use Excel to find theÂ 98%Â confidence interval for the mean electricity usage in kilowatt hours.Â Round your answers to two decimal placesÂ and use ascending order

QUESTION 22

Hugo averagesÂ 45Â words per minute on a typing test with a standard deviation ofÂ 12Â words per minute. Suppose Hugo’s words per minute on a typing test are normally distributed. LetÂ X=Â the number of words per minute on a typing test. Then,Â Xâˆ¼N(45,12).

Suppose Hugo typesÂ 47Â words per minute in a typing test on Wednesday. TheÂ z-score whenÂ x=47Â is ________. ThisÂ z-score tells you thatÂ x=47Â is ________ standard deviations to the ________ (right/left) of the mean, ________.

Correctly fill in the blanks in the statement above.

• Suppose Hugo typesÂ 47Â words per minute in a typing test on Wednesday. TheÂ z-score whenÂ x=47Â isÂ âˆ’0.167. ThisÂ z-score tells you thatÂ x=47Â isÂ 0.167Â standard deviations to theÂ leftÂ of the mean,Â 45.
• Suppose Hugo typesÂ 47Â words per minute in a typing test on Wednesday. TheÂ z-score whenÂ x=47Â isÂ 0.133. ThisÂ z-score tells you thatÂ x=47Â isÂ 0.133Â standard deviations to theÂ rightÂ of the mean,Â 45.
• Suppose Hugo typesÂ 47Â words per minute in a typing test on Wednesday. TheÂ z-score whenÂ x=47Â isÂ 0.167. ThisÂ z-score tells you thatÂ x=47Â isÂ 0.167Â standard deviations to theÂ rightÂ of the mean,Â 45.
• Suppose Hugo typesÂ 47Â words per minute in a typing test on Wednesday. TheÂ z-score whenÂ x=47Â isÂ âˆ’0.133. ThisÂ z-score tells you thatÂ x=47Â isÂ 0.133Â standard deviations to theÂ leftÂ of the mean,Â 45.

QUESTION 23

Hugo averagesÂ 42Â words per minute on a typing test with a standard deviation ofÂ 5.5Â words per minute. Suppose Hugo’s words per minute on a typing test are normally distributed. LetÂ X=Â the number of words per minute on a typing test. Then,Â Xâˆ¼N(42,5.5).

Suppose Hugo typesÂ 60Â words per minute in a typing test on Wednesday. TheÂ z-score whenÂ x=60Â is ________. ThisÂ z-score tells you thatÂ x=60Â is ________ standard deviations to the ________ (right/left) of the mean, ________.

Correctly fill in the blanks in the statement above.

• Suppose Hugo typesÂ 60Â words per minute in a typing test on Wednesday. TheÂ z-score whenÂ x=60Â isÂ 3.176. ThisÂ z-score tells you thatÂ x=60Â isÂ 3.176Â standard deviations to theÂ rightÂ of the mean,Â 42.
• Suppose Hugo typesÂ 60Â words per minute in a typing test on Wednesday. TheÂ z-score whenÂ x=60Â isÂ 3.273. ThisÂ z-score tells you thatÂ x=60Â isÂ 3.273Â standard deviations to theÂ rightÂ of the mean,Â 42.
• Suppose Hugo typesÂ 60Â words per minute in a typing test on Wednesday. TheÂ z-score whenÂ x=60Â isÂ âˆ’3.273. ThisÂ z-score tells you thatÂ x=60Â isÂ 3.273Â standard deviations to theÂ leftÂ of the mean,Â 42.
• Suppose Hugo typesÂ 60Â words per minute in a typing test on Wednesday. TheÂ z-score whenÂ x=60Â isÂ âˆ’3.176. ThisÂ z-score tells you thatÂ x=60Â isÂ 3.176Â standard deviations to theÂ leftÂ of the mean,Â 42.

QUESTION 24

Lisa has collected data to find that the number of pages per book on a book shelf has a normal distribution. What is the probability that a randomly selected book has fewer thanÂ 144Â pages if the mean isÂ 186Â pages and the standard deviation isÂ 21Â pages? Use the empirical rule. Enter your answer as a percent rounded to two decimal places if necessary.