Week 6 Math 225n Statistics Quiz Chamberlain College of Nursing MATH 225N 2024/2025 CORR, Exams of Mathematics

Download Week 6 Math 225n Statistics Quiz Chamberlain College of Nursing MATH 225N 2024/2025 CORR and more Exams Mathematics in PDF only on Docsity! Week 6 Math 225n Statistics Quiz Chamberlain College of Nursing MATH 225N That is correct! That is correct! Answer: ( 0.10, 0.18) Week 6 Math 225n Statistics Quiz Chamberlain College of Nursing MATH 225N 2024/2025 CORRECT ANSWERS STUDY SET 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. Answer: (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. Week 6 Math 225n Statistics Quiz Chamberlain College of Nursing MATH 225N That is correct! 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? 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. 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? Round up to the nearest integer. Answer: 14 dog heights 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 z0.02 5 z0.01 z0.005 1.28 1.64 1.96 2.32 2.57 That is correct! Week 6 Math 225n Statistics Quiz Chamberlain College of Nursing MATH 225N That is correct! Answer: (69.14, 71.38) That is correct! Answer: 53 dog heights That is correct! 72 69 72 72 71 HelpCopy to ClipboardDownload CSV 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 955.7and 1454.1 sq ft. Round your answer to the nearest whole number (percent). Answer: 95% Question 12 Week 6 Math 225n Statistics Quiz Chamberlain College of Nursing MATH 225N That is correct! That is correct! Answer: 0.9804 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. A B C 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 Week 6 Math 225n Statistics Quiz Chamberlain College of Nursing MATH 225N That is correct! 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. σx¯=6 games σx¯=3 games σx¯=4 games μx¯=18 games μx¯=3 games μx¯=9 games Answer: 38.12 That is correct! Week 6 Math 225n Statistics Quiz Chamberlain College of Nursing MATH 225N That is correct! Answer: 0.26 B has the larger standard deviation. The standard deviations of A and B 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 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: Answer: μ=58 σ=18 n= 36 μx=58 σx=3 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? Week 6 Math 225n Statistics Quiz Chamberlain College of Nursing MATH 225N That is correct! 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 HelpCopy to ClipboardDownload CSV Answer: (894.43, 940.21) Question 22 Hugo averages 40 words per minute on a typing test with a standard deviation of 15 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(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. Suppose Hugo types 56 words per minute in a typing test on Wednesday. The z-score when x=56 is −0.889. This z-score tells you that x=56 is 0.889 standard deviations to the left of the mean, 40. That is correct! Week 6 Math 225n Statistics Quiz Chamberlain College of Nursing MATH 225N Suppose Hugo types 56 words per minute in a typing test on Wednesday. The z-score when x=56 is −1.067. This z-score tells you that x=56 is 1.067 standard deviations to the left of the mean, 40. Suppose Hugo types 56 words per minute in a typing test on Wednesday. The z-score when x=56 is 1.067. This z-score tells you that x=56 is 1.067 standard deviations to the right of the mean, 40. Suppose Hugo types 56 words per minute in a typing test on Wednesday. The z-score when x=56 is 0.889. This z-score tells you that x=56 is 0.889 standard deviations to the right of the mean, 40. Question 23 Hugo averages 62 words per minute on a typing test with a standard deviation of 8 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(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. Suppose Hugo types 56 words per minute in a typing test on Wednesday. The z-score when x=56 is 0.75. This z-score tells you that x=56 is 0.75 standard deviations to the right of the mean, 62. Suppose Hugo types 56 words per minute in a typing test on Wednesday. The z-score when x=56 is −0.75. This z-score tells you that x=56 is 0.75 standard deviations to the left of the mean, 62. Suppose Hugo types 56 words per minute in a typing test on Wednesday. The z-score when x=56 is 0.545. This z-score tells you that x=56 is 0.545 standard deviations to the right of the mean, 62. Suppose Hugo types 56 words per minute in a typing test on Wednesday. The z-score when x=56 is −0.545. This z-score tells you that x=56 is 0.545 standard deviations to the left of the mean, 62. That is correct!