Please please help me with all parts, I have only one last attempt. Thank you so much!

Q 1.

Suppose that a category of world class runners are known to run a marathon (26 miles) in an average of 146 minutes with a standard deviation of 16 minutes. Consider 49 of the races. Let )7 = the average of the 49 races. Give the distribution of )7. (Round your standard deviation to two decimal places.) 7~l:](l:].l:l) Find the probability that the average of the sample will be between 143 and 147 minutes in these 49 marathons. (Round your answer to four decimal places.) |H Find the 70th percentile for the average of these 49 marathons. (Round your answer to two decimal places.) Find the median of the average running times. 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 sample mean wait time was seven hours with a sample standard deviation of three hours. Part (a) (i) Enter an exact number as an integer, fraction, or decimal. X = hrs (ii) Enter an exact number as an integer, fraction, or decimal. SX = hrs (iii) 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 amount of time an individual waits at the courthouse to be called for service. X is the mean wait time for a sample of individuals. O X is the amount of time an individual waits at the courthouse to be called for service. X is the mean wait time for a sample of individuals. 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 number of individuals at the courthouse to be called for service. X is the average number of individuals at the courthouse.El Part (c) Which distribution should you use for this problem? (Enter your answer in the form 2 or tdfwhere df is the degrees of freedom.) S Explain your choice. 0 The Student's t-distribution for 81 degrees of freedom should be used because the sample standard deviation is known. 0 The standard normal distribution should be used because the population standard deviation is known, 0 The Student's tdistribution for 80 degrees of freedom should be used because we do not know the population standard deviation. 0 The standard normal distribution should be used because the sample standard deviation is known. - Part (d) Construct a 95% confidence interval for the population mean time wasted. (i) State the confidence interval. (Round your answers to two decimal places.) hrs (ii) Sketch the graph. (Round your answers to two decimal places. Enter your a/2 to three decimal places.) CL = = N / 8 N 8 = X (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. 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. We are 95% confident 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. There is a 95% chance that a wait time at the courthouse lies within this interval