Question: [10 marks] Suppose that you measure the weights of 24 male runners and that you do not actually choose an SRS, but you are willing to assume that these runners are a random sample from the population of male runners in your city. Here are their weights in kilograms:

a. [2 marks] What is \({{\sigma }_{{\bar{X}}}}\) the standard deviation of \(\bar{X}\) ?

b. [4 marks] Give a 95% CI for \(\mu \), the mean of the population from which the sample is drawn.

c. [4 marks] Are you quite sure that the average weight of the population of runners is less than 65 kg? Why or why not?