Question

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.

Answer 1

Answer:

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:

$\lambda=4\;\text{cars/half an hour}=8\;\text{cars/hour}$

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

$P(x=k)=8^{k} \cdot e^{-8}/k!$

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

$P(5)=8^{5} \cdot e^{-8}/5!=32768*0.0003/120=0.0920$

Answer 2

The probability that, in an hour, exactly 5 cars will enter the car wash will be 0.0920.

What is probability?

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1.

Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.

The mean rate is found as;

$\rm \lambda =4 \ cars / half \ an \ hour = 8 car / hour$

The probability that exactly k cars will enter the car wash

$P(x=K) = \frac{8^k e^{-8}}{k\!}\\\\P(x=5) = \frac{8^5 e^{-8}}{5\!}\\\\ P(x=5)=0.0920$

Hence the probability that, in an hour, exactly 5 cars will enter the car wash will be 0.0920.

To learn more about the probability link is given below.

https://brainly.com/question/795909

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