1. In a class of 80 students, the professor calls on 1 student chosen at random for a recitation in each class period. There are 32 class periods in a term.
  1. Write a formula for the exact probability that a given student is called upon j times during the term.

ans: \(b(32, j, 1/80) = (32/j)* (1/80)^j * (79/80)^(32-j)\)

  1. Write a formula for the Poisson approximation for this probability. Using your formula estimate the probability that a given student is called upon more than twice.

\(λ = 32/80 = 2/5\)

probability that a student will be called on more \(j\) times: \(e^(-2/5)*(2/5)^j / j!\)

So, the approximate probability that a student is called on more than twice: \(1-e^(-2/5)\)*\[\left(\begin{array} {rr} (2/5)^0/0! + (2/5)^1/1! + (2/5)^2/2!\end{array}\right)\] = .0079