Discussion 7

N Nedd

2017-10-10

Section 5.1 #21

Answer

Let X represent the event that a given student is called.

X ~ B(32, 1/80)

Part a

P(X = j) = \(\frac{32!}{j!(32-j)!}\quad (\frac{1}{80})^j \quad(1 - \frac{1}{80})^{32-j}\)

Part b

For poisson approximation of binomial distribution:

X ~ P(32 x 1/80) = X ~ P(0.4)

P(X = j)

\(\frac{e^{-0.4}\quad0.4^j}{j!}\)

P(X > 2) = 1 - P(X <= 2) = 1 - [P(X=0) + P(X=1) + P(X=2)]

Prob0 <- (exp(-0.4) * 0.4^0)/factorial(0)
Prob1 <- (exp(-0.4) * 0.4^1)/factorial(1)
Prob2 <- (exp(-0.4) * 0.4^2)/factorial(2)
Ans <- 1- (Prob0 + Prob1 + Prob2)
Ans

## [1] 0.007926332