MATH 225N Week 6 Statistics Quiz

1.     A statistics professor recently graded final exams for students in her introductory statistics course. In a review of her grading, she the mean score out of … 100points 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.

2.     A random sample of adults was… 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.

3.    The pages per book in a library are normally … 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?

4.    The population standard deviation for the heights of dogs, in inches, in a city is 7inches. If we want to be 95% … that the sample mean is within 2 inches of the true population mean, what is the minimum sample size that can take? Round up to the nearest integer.

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 poll to create the confidence interval?

6.   The average score of a … random sample of 87senior 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..

7.   A random sample of 28statistics tutorials was 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% Round your answers to two decimal places and use increasing order.

8.   Eric is studying people’s typing habits. He surveyed 525people 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.

9.   A sample of 27employees 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.

10. The population standard deviation for the heights of dogs, in inches, in a city is 7inches. 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.

11. A random sample of house sizes in major city has a sample mean of x¯=1204.9sq ft and sample standard deviation of s=124.6sq ft.  Use the Empirical Rule to determine the approximate percentage of house sizes that lie between 7and 1454.1 sq ft…… Round your answer to the nearest … whole number (percent).

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.

13. The resistance of a strain gauge is normally distributed with a mean of 100ohms and a standard deviation of 3ohms. 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.

14. A baker knows that the daily demand for strawberry pies is a random variable that follows the normal distribution with a … mean of 8pies and a standard deviation of 4.5pies. Find the demand that has an 8% probability of being exceeded………Use Excel, and round your answer to two decimal places.

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 18games, with a population standard deviation of 6If a sample … of only 2 friends is … 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.

16. An elementary school has a population of 635students, 600of 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.

17. The lengths of text messages are normally … 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?

18. Given the plot of normal distributions Aand Bbelow, which of the following statements is true? Select all correct answers. A normal bell curve labeled Upper A and a normal elongated curve labeled Upper B are at the same point. Normal curve Upper B is narrower and above normal curve Upper A.

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 36tours, identify each of the following to help them make their decision and round to the nearest hundredth if necessary: 

20. From a recent company survey, it is … that the proportion of employees older than 55and 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?

21. In order to estimate the average electricity usage per month, a sample of 125residential customers were … , and the monthly electricity usage was … 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.

22. Hugo averages 40words per minute on a typing test with a standard deviation of 15words per minute. Suppose Hugo’s words per minute on a typing test are normally … Let X= the number of words per minute on a typing test. Then, X∼N(40,15)……..Suppose Hugo types 56 words per minute in a typing test on Wednesday. The z-score when x=56 is ________. This z-score tells you that x=56 is ________ standard deviations to the ________ (right/left) of the mean, ________……..Correctly fill in the blanks in the statement above.

23. Hugo averages 62words per minute on a typing test with a standard deviation of 8words per minute. Suppose Hugo’s words per minute on a typing test are normally … Let X= the number of words per minute on a … typing test. Then, X∼N(62,8)…….Suppose Hugo types 56 words per minute in a typing test on Wednesday. The z-score when x=56 is ________. This z-score tells you that x=56 is ________ standard deviations to the ________ (right/left) of the mean, ________………Correctly fill in the blanks in the statement above.

24. Lisa has collected data to find that the number of pages per book on a bookshelf has a normal distribution. What is the probability that a random… book has fewer than 168pages if the mean is 190pages and the … standard deviation is 22 pages? Use the empirical rule. Enter your answer as a percent rounded to two decimal places if necessary.

25. Lisa has collected data to find that the number of pages per book on a bookshelf has a normal distribution. What is the probability that a random… book has fewer than 140pages if the mean is 190pages and the standard deviation is 25 pages? Use the empirical rule. Enter your answer as a percent rounded to … two decimal places if necessary.