Announcements for 82 upcoming engineering conferences were randomly picked from a stack of IEEE Spectrum magazines. The mean length of the conferences was 3.92 days. The population standard deviation is 1.26 days. Assume the underlying population is normal. Part (a) In words, define the random variables X and X. O X is the mean number of engineering conferences listed in IEEE Spectrum magazine, and X is the number of engineering conferences. O X is the number of engineering conferences, and X is the mean number of engineering conferences listed in IEEE Spectrum magazine. 82 engineering conferences, and X is the length of an engineering conference. O X is the length of an engineering conference, and X is the mean length from a sample of 82 engineering conferences. part (b ) Which distribution should you use for this problem? Explain your choice. The Student's t-distribution should be used because the sample mean is smaller than 30. The s The Student's t-distribution should be used because the sample standard deviation is given The standard normal distribution should be used because the population standard deviation is known. Part (c) Construct a 95% confidence interval for the population mean length of engineering conferences. (1) State the confidence interval. (Round your answers to two decimal places.) (ii) Sketch the graph. (Round your answers to two decimal places. Enter your a/2 to three decimal places.) a C.L. = X (i) Calculate the error bound. (Round your answer to two decimal places.) [-/5 Points] DETAILS ILLOWSKYINTROSTAT1 8.2.106.HW. MY NOTES ASK YOUR TEACHER Suppose that a committee is studying whether or not there is waste of time in our judicial system. It is interested in the mean amount of time individuals waste at the courthouse waiting to be called for jury duty. The committee randomly surveyed 81 people who recently served as jurors. The ample mean wait time was seven hours with a sample standard deviation of four hours. Part (a ) () Enter an exact number as an integer, fraction, or decimal. * = hrs (i) Enter an exact number as an integer, fraction, or decimal. SX = hrs (i) Enter an exact number as an integer, fraction, or decimal. n= (iv) Enter an exact number as an integer, fraction, or decimal. n- 1 = Part (b) (b) Define the random variables X and X in words. O X is the number of individuals at the courthouse to be called for service. X is the average number of individuals at the courthouse. O X is the amount of time an ime for a sample of individuals. O X is the amount of time an individual waits at the cou e called for service. X is the mean wait time for a sample of individuals. O X is the number of individuals at the cou of individuals at the courthouse. Part (c) Which distribution should you use for this problem? (Enter your answer in the form z or tay Where of is the degrees of freedom.) Explain your choice. The Student's t-distribution for 81 cause the sample standard deviation is known. O The standard normal distribu standard deviation is known. O The standard normal distribution shou standard deviation is known. The Student's t-distribution for 80 deg because we do not know the population standard deviation. Part (d) Construct a 95% confidence interval for the population mean time wasted. (1) State the confidence interval. (Round your answers to two decimal places.) (i) Sketch the graph. (Round your answers to two decimal places. Enter your @/2 to three decimal places.) CL = iii) Calculate the error bound. (Round your answer to two decimal places.) hrs Part (e) Explain in a complete sentence what the confidence interval means. There is a 95% chance that a wait time at the courthouse lies within this interval. O We are 95% confident that the true population mean wait time at the courthouse lies within this interval. O We are 95% confident that a wait time at the courthouse lies within this interval. We are 95% confident that the mean wait time at the courthouse of the sample of 81 individuals waiting at the courthouse lies within this interval