The number of streets in the downtown section of a certain city that need repairs in a given year is a random variable with a distribution described by the probability density function Find the probability that at most half of the streets will need repairs in any given year.

Question

The number of streets in the downtown section of a certain city that need repairs in a given year is a random variable with a distribution described by the probability density function  Find the probability that at most half of the streets will need repairs in any given year.

Quizplus · Accepted Answer

We need to find the probability that at most half of the streets need repairs, which means we need to find the probability that X ≤ 50 (where X is the number of streets needing repairs). To do this, we need to integrate the given probability density function from 0 to 50:

P(X ≤ 50) = ∫0^50 0.00022x^2 e^(-0.0011x) dx

This integral can be evaluated using integration by parts, or by using a table of integrals. Either way, we get:

P(X ≤ 50) ≈ 0.6604

So the answer is C, 11eaa8b1_da03_7a2c_b1b6_29f115c46b11_TB6026_11.

The Number of Streets in the Downtown Section of a Certain