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 3 students will have their automobiles stolen during the current semester?

Answer: 0.9577 ≈ 95.77%

Step-by-step explanation:

This can be solved by the Poisson distribution formula for random variables when the mean outcome of such variables are given.

The Poisson Formula is denoted by:

P (X=K) = e^-λ * (λ^k/k!)

Where e = exponential factor y 2.71828

λ = mean / average outcome = 8

k = varied outcome.

To find the probability of more than 3, we find the probability of 3 or less, sum it then subtract from 1, that is P (X>3) = 1 - P (X≤3)

When k=0

P (X=0) = e^-8 * (8^0/0!) = 0.000335

When k=1

P (X=1) = e^-8 * (8¹/1!) = 0.00268

When k=2

P (X=2) = e^-8 * (8²/2!) = 0.0107

When k=3

P (X=3) = e^-8 * (8³/3!) = 0.0286

P (X≤3) = 0.00035 + 0.00268 + 0.0107 + 0.0286 = 0.0423

Hence, P (X>3) = 1 - 0.0423 = 0.9577 ≈ 95.77%