Midterm

\[ Part 1 \]

plot(x=0:10,dpois(0:10,4.5),main="PMF of Poisson",xlab="n",ylab="Probability")

Free 5 points

\[3 or fewer\]

ppois(3,4.5)

## [1] 0.342296

This probability is found using poisson where 4.5 is our average and 3 is the probability of everything up to 3

pexp(2,.1875)

## [1] 0.3127107

This probabilty is found using pexp where 2 is the time or q and .1875 is the average

\[Part2\]

curve(dnorm(x,200,30),from=120,to=280,
      main="Normal distribution with mean 200 and sd 30",
      ylab="f(x)",
      xlab="x")

above shows a mean of 200 with Q1 being 150 and Q2 being 250 with a SD of 30 grams

pnorm(150,200,30)

## [1] 0.04779035

This probability is found by using pnorm where 150 is the probability of less than 150. 200 is the mean and 30 is the SD