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 score out of 100 points was a x¯=77, with a margin of error of 10.
Construct a confidence interval for the mean score (out of 100 points) on the final exam.
Question 2
A random sample of adults were asked whether they prefer reading an e-book over a printed book. The survey resulted in a sample proportion of p′=0.14, with a sampling standard deviation of σp′=0.02, who preferred reading an e-book.
Use the empirical rule to construct a 95% 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 a 95% confidence interval of (237,293) pages.
What is the correct interpretation of the 95% confidence interval?
Question 4
The population standard deviation for the heights of dogs, in inches, in a city is 3.7 inches. If we want to be 95% confident that the sample mean is within 2 inches of the true population mean, what is the minimum sample size that can be taken?
Use the table above for the 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 a 98% confidence interval which has an error bound of at most 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 of 87 senior business majors at a university who took a certain standardized test follows a normal distribution with a standard deviation of 28. Use Excel to determine a 90% confidence interval for the mean of the population. Round your answers to two decimal places and use ascending order.
Score
516
536
462
461
519
496
517
488
521
487
535
473
524
535
501
474
485
548
463
514
505
460
499
534
539
534
489
520
451
481
559
564
514
461
504
534
510
538
501
607
509
554
547
474
566
560
429
484
492
495
556
534
504
476
539
543
551
497
514
530
559
472
459
493
555
512
515
503
530
560
562
482
582
523
535
509
471
513
503
516
534
499
525
559
459
509
587
Question 7
A random sample of 28 statistics tutorials was selected from the past 5 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 past 5 years with 90% confidence. Round your answers to two decimal places and use increasing order.
Number of Absences
13.9
16.4
12.3
13.2
8.4
4.4
10.3
8.8
4.8
10.9
15.9
9.7
4.5
11.5
5.7
10.8
9.7
8.2
10.3
12.2
10.6
16.2
15.2
1.7
11.7
11.9
10.0
12.4
Question 8
Eric is studying people’s typing habits. He surveyed 525 people and asked whether they leave one space or two spaces after a period when typing. 440 people responded that they leave one space. Create a 90% 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 of 27 employees for the Department of Health and Human Services has the following salaries, in thousands of dollars. Assuming normality, use Excel to find the 98% confidence interval for the true mean salary, in thousands of dollars. Round your answers to two decimal places and use increasing order.
Salary
71
70
69
65
72
69
72
72
71
72
73
66
68
71
71
69
70
72
72
71
68
68
75
73
71
66
70
Question 10
The population standard deviation for the heights of dogs, in inches, in a city is 3.7 inches. If we want to be 95% confident that the sample mean is within 1 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 the 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 of x¯=1204.9 sq ft and sample standard deviation of s=124.6 sq ft. Use the Empirical Rule to determine the approximate percentage of house sizes that lie between 955.7 and 1454.1 sq ft.
Round your answer to the nearest whole number (percent).
Question 12
The graph below shows the graphs of several normal distributions, labeled A, B, and 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 of 100 ohms and a standard deviation of 0.3 ohms. To meet the specification, the resistance must be within the range 100±0.7 ohms. What proportion of gauges is acceptable?
- Round your answer to four decimal places.
Question 14
A baker knows that the daily demand for strawberry pies is a random variable that follows the normal distribution with a mean of 31.8 pies and a standard deviation of 4.5 pies. Find the demand that has an 8% probability of being exceeded.
- Use Excel, and round your answer to two decimal places.
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 of 18 games, with a population standard deviation of 6 games. If a sample of only 2 friends is selected at random from the group, select the expected mean and the standard deviation of the sampling distribution from the options below. Remember to round to the nearest whole number.
Question 16
An elementary school has a population of 635 students, 600 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 size 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 a 95% confidence interval of (23,47) characters.
What is the correct interpretation of the 95% confidence interval?
Question 18
Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers.
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 is $58, with a standard deviation of $18. If they take a random sample of 36 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 than 55 and considering retirement is 8%. For a random sample of size 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 of 125 residential customers were selected, and the monthly electricity usage was determined using the customers’ meter readings. Assume a population variance of 12,100kWh2. Use Excel to find the 98% confidence interval for the mean electricity usage in kilowatt hours. Round your answers to two decimal places and use ascending order.
Electric Usage
765
1139
714
687
1027
1109
749
799
911
631
975
717
1232
806
637
894
856
896
1272
1224
621
606
898
723
817
746
933
595
851
1027
770
685
750
1198
975
678
1050
886
826
1176
583
841
1188
692
733
791
584
1163
593
1234
603
1044
1233
1178
598
904
778
693
590
845
893
1028
975
788
1240
1253
854
1185
1164
741
1058
1053
795
1198
1240
1140
959
938
1008
1035
1085
1100
680
1006
977
1042
1252
943
1165
1014
912
791
612
935
864
953
667
1005
1063
1095
1086
810
1032
970
1099
1229
892
1074
579
754
1007
1116
583
763
1231
966
962
1132
738
1033
697
891
840
725
1031
Question 22
Hugo averages 42 words per minute on a typing test with a standard deviation of 9.5 words per minute. Suppose Hugo’s words per minute on a typing test are normally distributed. Let X= the number of words per minute on a typing test. Then, X∼N(42,9.5).
Suppose Hugo types 72 words per minute in a typing test on Wednesday. The z-score when x=72 is ________. This z-score tells you that x=72 is ________ standard deviations to the ________ (right/left) of the mean, ________.
Correctly fill in the blanks in the statement above.
Question 23
Hugo averages $_41$_ words per minute on a typing test with a standard deviation of $_12$_ words per minute. Suppose Hugo’s words per minute on a typing test are normally distributed. Let $_X = $_ the number of words per minute on a typing test. Then, $_X \sim N(41, 12)$_.
Suppose Hugo types $_62$_ words per minute in a typing test on Wednesday. The $_z$_-score when $_x = 62$_ is ________. This $_z$_-score tells you that $_x = 62$_ is ________ standard deviations to the ________ (right/left) of the mean, ________.
Correctly fill in the blanks in the statement above.
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 than $_169$_ pages if the mean is $_194$_ pages and the standard deviation is $_25$_ pages? Use the empirical rule. Enter your answer as a percent rounded to two decimal places if necessary.
Question 25
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 than $_151$_ pages if the mean is $_193$_ pages and the standard deviation is $_21$_ pages? Use the empirical rule.Enter your answer as a percent rounded to two decimal places if necessary.
Solution
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 score out of 100 points was a x¯=77, with a margin of error of 10.
Construct a confidence interval for the mean score (out of 100 points) on the final exam.
Ans: (67, 87)
Question 2
A random sample of adults were asked whether they prefer reading an e-book over a printed book. The survey resulted in a sample proportion of p′=0.14, with a sampling standard deviation of σp′=0.02, who preferred reading an e-book.
Use the empirical rule to construct a 95% confidence interval for the true proportion of adults who prefer e-books.
Ans: (0.10, 0.18)
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 a 95% confidence interval of (237,293) pages.
What is the correct interpretation of the 95% confidence interval?
Ans: We estimate with 95% confidence that the true population mean is between 237 and 293 pages…………..please follow the link below to purchase the solution at $20
