Answer 5 and 6, using R programming code:

5. We have seen the following functions dnorm normal probability density function pnorm normal cumulative distribution function qnorm normal quantile function a. Let X have a normal distribution with mean 100 and variance 100. Find the 90th percentile of X by calling the function qnorm in two ways: (i) specify the arguments by position, and (ii) specify the arguments by complete names. b. Find P(X > 90) using the function pnorm in two ways: (i) without the use of the optional argument lower.tail, and (ii) with the use of the optional argument lower.tail but no additional arithmetic operation. 6. Let X have a Poisson distribution with parameter 1 = 3, the name for the Poisson distribution on R is pois, using one function per point find a. P(X = 4) b. P(X 2)