Question

The number of students who enroll in a psychology course is a Poisson random variable with mean 105. The professor in charge of the course has decided that if the number enrolling is 119 or more, the course will be taught in two sections, whereas if fewer than 119 students enroll, the students will be all taught together in a single section. What is the probability that the professor will have to teach two sections?

Answer 1

The answer is "0.096".

Explanation:

In this question, the X is a number of the students who enroll in a psycholog y course, follows a Poisson distribution with mean
`= \lambda= 105`

`\therefore P(X=x)=(e^(-105) 105^(x))/(x!),(x=0,1,2,3.....)\\\\\to p(teach\ two \ sections) = P(X \geq 119)\\\\=1-P(X<119)\\\\=1-\sum_(x=0)^(118)P(X=x)\\\\=1-\sum_(x=0)^(118)(e^(-105) 105^(x))/(x!)\\\\=0.0956747863537\\\\=0.096\\`