CONFIDENTIAL CS/FEB 2022/STA416 QUESTION 3 a) The waiting time at an. elevator in a shopping mall is approximately normally distributed with a mean of 3.2 minutes and a standard deviation of 1.5 minutes. i) What is the probability if the waiting time is at most 2.8 minutes? (2 marks) iii) Find the probability that the waiting time is more than 3 minutes. (3 marks) i) Find the value of k if 95% of all the customers are having waiting time of less than k minutes. (3 marks) b) An important factor in solid missile fuel is the particle size distribution. Based on the production data in the past, it has been determined that the particle size (in micrometers) distribution, X is having the following probability density function. f (x) = (12x*(1 -x) ;OSxs1 ; others i) State the type of the random variable X and calculate the expected value of X. (4 marks) ii ) Find P(X 1). (4 marks) m w 32C Light rain ASUS