Cars enter a car wash at a mean rate of 4 cars per half an hour. What is the probability that, in any hour, exactly 5 cars will enter the car wash? Round your answer to four decimal places.

The probability that, in any hour, exactly 5 cars will enter the car wash is P(x=5)=0.0920.

Step-by-step explanation:

This can be modeled as a Poisson random variable.

The mean rate is the parameter of the Poisson distribution:

The probability that exactly k cars will enter the car wash can be calculated as:

Then, the probability that exactly 5 cars will enter the car wash is:

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50