Let Y N(8, 4). Compute each of the following, in terms of the function of Definition 2.5.2 and use software R to evaluate these probabilities numerically. (a) P(Y 5) (b) P(2 Y 7) (c) P(Y 3)

Use the pnorm function in R.

d) Find the 40th and 77th percentiles. Use the qnorm function in R

Definition 2.5.2 The symbol d stands for the cumulative distribution function of a standard normal distribution, defined by X X p(t) di = -12/2 dt , (2.5.2) D (x) = V2x for x E Rl