explain the answers please

I'EJE 1 1o 63 On August 29, 2021, University U tested 2,790 incoming students for COVID-19. Three were found to be positive. It was thus estimated that 0.11% of the arriving students will be infected. With a total of 13,500 students, this amounts to 15 positive cases. The students who test positive will have to be placed in isolation units, and the university must ensure that enough units are available. To be on the safe side, U decides to set aside as many units as indicated by the 99% condence interval. The number of isolation units is 045 060 040 030 I'l 2 1o 63 X,- e {0, 1}, i = 1, , n, are independent random variables, each having P{X,- = 1} = p = 0.1, and Y = % 221:1 X,- is their sample mean. Which of the following statements are true? Y is a discrete random variable. : The variance of Y is np(1 p). Y is Gaussian distributed. If np(1 p) >> 1, the distribution of Y can be approximated as Gaussian