Question

Suppose that on the average, 8 students enrolled in a small liberal arts college have their automobiles stolen during the semester. What is the probability that more than 1 student will have his automobile stolen during the current semester? Round your answer to four decimal places.

Answer 1

Answer:

P(X > 1) = 0.9970

Explanation:

The average number of students, λ = 8

Using the poisson distribution formula:

$\begin{gathered} P(X=x)=\frac{(e^{-\lambda}\lambda^x)}{x!} \\ \end{gathered}$

Probability that more than 1 student will have his automobile stolen during the current semester is P(X > 1)

P(X > 1) = 1 - (PX ≤ 1)

P(X≤1) = P(X=0) + P(X=1)

$\begin{gathered} P(X=0)=\frac{(e^{-8})(8^0)}{0!} \\ \\ P(X=0)=0.000335 \\ \\ P(X=1)=\frac{(e^{-8})(8^1)}{1!} \\ \\ P(X=1)=0.00268 \end{gathered}$

P(X≤1) = 0.000335 + 0.00268

P(X≤1) = 0.003015

P(X > 1) = 1 - (PX ≤ 1)

P(X > 1) = 1 - 0.003015

P(X > 1) = 0.9970