Answer to Question #144817 in Statistics and Probability for Nikiwe Makhubele

Question

Find the probability that 5 students seek assistance in a month

Answer 1

The number of students who seek assistance with their Statistics assignments is Poisson distributed with a mean of two per day.

Find the probability that 5 students seek assistance in a month.

Let $X=$ the number of students who seek assistance with their Statistics assignments: $X\sim Po(\lambda t)$

$$P(X=x)=\dfrac{e^{-\lambda t}(\lambda t)^x}{x!}$$

Given $\lambda=2/day, t=30\ days$

$$P(X=5)=\dfrac{e^{-2(30)}(2(30))^5}{5!}\approx0$$

The probability that 5 students seek assistance in a month is approximately zero.