Suppose that we select forty random numbers, independently, from the interval [1,5]. Hint: This is a random sample X₁, X₂, ... , X₄₀ from the uniform distribution on [1.5].
(a) Find the expected value and variance of the sum (i.e., the sample total).
(b) Find the approximate probability that the sum is greater than 135.
(c) Find an interval which includes the value of the sum with an approximate probability of 68.3%.