The standard background of observed neutrons is almost entirely from cosmicrays

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 larger than 9.684?

c. Find the 99.5th percentile of the distribution the sample mean number of neutrons per

one second interval in this case.

d. The researcher collected some data decided to compute a 90% confidence 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, , is in the interval found by the researcher". Is this

statement correct? Why or why not? Explain.