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MAT 130 MODULE 4 CHECK YOUR UNDERSTANDING 1. Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution. A certain question on a test is answered correctly by 22% of the respondents. Estimate the probability that among the next 150 responses there will be at most 40 correct answers. 2. Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. n = 130, x = 65; 90% 3. Find the indicated probability. The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter greater than 0.32 inches? 4. Solve the problem. Round to the nearest tenth unless indicated otherwise. Scores on an English test are normally distributed with a mean of 33.8 and a standard deviation of 8.5. Find the score that separates the top 59% from the bottom 41%. n. 5. Use the confidence level and sample data to find a confidence interval for estimate the population ?. Round your answer to the same number of decimal places as the sample mean. A group of 68 randomly selected students have a mean score of 27.3 with a standard deviation of 2.1 on a placement test. What is the 90% confidence interval for the mean score, , of all students taking the test? 6. Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level. Round the margin of error to four decimal places. 95% confidence; n = 2448, x = 1763 7. Use the confidence level and sample data to find the margin of error E. Round your answer to the same number of decimal places as the sample mean unless otherwise noted. The duration of telephone calls directed by a local telephone company: = 4.2 minutes, n = 500, 97% confidence. Round your answer to the nearest thousandth. . 8. Suppose that replacement times for washing machines are normally distributed with a mean of 9.3 years and a standard deviation of 1.1 years. Find the probability that 70 randomly selected washing machines will have a mean replacement time less than 9.1 years. 9. Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. Of 375 randomly selected medical students, 30 said that they planned to work in a rural community. Find a 95% confidence interval for the true proportion of all medical students who plan to work in a rural community. 10. Use the normal distribution to approximate the desired probability. A coin is tossed 20 times. A person, who claims to have extrasensory perception, is asked to predict the outcome of each flip in advance. She predicts correctly on 14 tosses. What is the probability of being correct 14 or more times by guessing? Does this probability seem to verify her claim? 11. Use the normal distribution to approximate the desired probability. A coin is tossed 20 times. A person, who claims to have extrasensory perception, is asked to predict the outcome of each flip in advance. She predicts correctly on 11 tosses. What is the probability of being correct 11 or more times by guessing? Does this probability seem to verify her claim? n. 12. The scores on a certain test are normally distributed with a mean score of 51 and a standard deviation of 2. What is the probability that a sample of 90 students will have a mean score of at least 51.2108? 13. Use the given information to compute a confidence interval for the population mean. 95% confidence; n = 32, = 137, = 2.3 a. 14. Use the given information to compute a confidence interval for the population mean. 99% confidence; n = 32, = 137, = 2.3 15. Solve the problem. The following confidence interval is obtained for a population proportion, p: 0.883 < p < 0.911. Use these confidence interval limits to find the margin of error, E. t Math Assignment Help, Math Homework help, Math Study Help, Math Course Help