Mathematics > Exam > MATH 225N Week 6 quiz (2020) – Chamberlain College of Nursing | MATH225N Week 6 quiz (2020) (All)

MATH 225N Week 6 quiz (2020) – Chamberlain College of Nursing | MATH225N Week 6 quiz (2020)

MATH 225N Week 6 quiz (2020) – Chamberlain College of Nursing QUESTION 1 1/1 POINTS A statistics professor recently graded final exams for students in her introductory statistics course. In a r... eview 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. That is correct! $$(67, 87) Answer Explanation Correct answers: • $\left(67,\ 87\right)$(67, 87)​ A confidence interval is an interval of values, centered on a point estimate, of the form (pointestimate−marginof error,pointestimate+marginof error) Using the given point estimate for the mean, x¯=77 and margin of error 10, the confidence interval is: (77−10,77+10)(67,87) QUESTION 2 1/1 POINTS A random sample of adults were asked whether they prefer reading an e-book over a printed book. The survey resulted in a sample proportion of p′=0.14, with a sampling standard deviation of σp′=0.02, who preferred reading an e-book. Use the empirical rule to construct a 95% confidence interval for the true proportion of adults who prefer e-books. That is correct! $$(0.10, 0.18) Answer Explanation Correct answers: • $\left(0.10,\ 0.18\right)$(0.10, 0.18)​ By the Empirical Rule, a 95% confidence interval corresponds to a z-score of z=2.  Substituting the given values p′=0.14 and σp′=0.02, a confidence interval is (p′−z⋅σp′,p′+z⋅σp′)(0.14−2⋅0.02,0.14+2⋅0.02)(0.14−0.04,0.14+0.04)(0.10,0.18) QUESTION 3 1/1 POINTS 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? That is correct! We estimate with 95% confidence that the sample mean is between 237 and 293 pages. We estimate that 95% of the time a book is selected, there will be between 237 and 293 pages. We estimate with 95% confidence that the true population mean is between 237 and 293 pages. Answer Explanation Correct answer: We estimate with 95% confidence that the true population mean is between 237 and 293 pages. Once a confidence interval is calculated, the interpretation should clearly state the confidence level (CL), explain what population parameter is being estimated, and state the confidence interval. We estimate with 95% confidence that the true population mean is between 237 and 293 pages. - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - QUESTION 24 1/1 POINTS 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 133 pages if the mean is 189 pages and the standard deviation is 28 pages? Use the empirical rule.Enter your answer as a percent rounded to two decimal places if necessary. That is correct! $$2.28% Answer Explanation Correct answers: • $2.5\%$2.5%​ Notice that 133 pages is two standard deviations less than the mean. Based on the empirical rule, 95% of the number of pages in the books are within two standard deviations of the mean. Since the normal distribution is symmetric, this implies that 2.5% of the number of pages in the books are less than two standard deviations less than the mean. QUESTION 25 1/1 POINTS Lisa has collected data to find that the number of pages per book on a book shelf has a normal distribution. What is the probability that a randomly selected book has fewer than 142 pages if the mean is 190 pages and the standard deviation is 24 pages? Use the empirical rule.Enter your answer as a percent rounded to two decimal places if necessary. That is correct! $$2.28% Answer Explanation Correct answers: • $2.5\%$2.5%​ Notice that 142 pages is two standard deviations less than the mean. Based on the empirical rule, 95% of the number of pages in the books are within two standard deviations of the mean. Since the normal distribution is symmetric, this implies that 2.5% of the number of pages in the books are less than two standard deviations less than the mean. [Show More]

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