6. (10 marks) The standard background of observed neutrons is almost entirely from cosmic- rays interacting With the surrounding environment and follows a distribution With a mean of 10 neutrons per second for a particular detector and a standard deviation of 3.16 neutrons. Suppose that a study is done by counting the number of neutrons in each of 169 one second intervals. a. What is the distribution of the sample mean number of neutrons per one second (give the name of the distribution and appropriate parameter values)? b. What is the probability that the sample mean number of neutrons per one second interval is lar er than 9.684? c. Find the 99.5 percentile of the distribution the sample mean nlunber of neutrons per one second interval in this case. d. The researcher collected some data decided to compute a 90% condence interval for the mean number of number of neutrons per one second interval. Consider the following statement: \"There is a 90% chance that the true mean number of neutrons per one second interval, as, is in the interval found by the researcher\". Is this statement correct? Why or why not? Explain