Question

Cars enter a car wash at a mean rate of 3 cars per half an hour. What is the probability that, in any hour, exactly 4 cars will enter the car wash? Round your answer to four decimal places.

Answer 1

Given: The mean rate of cars per half an hour is 3

To Determine: The probability that, in any hour, exactly 4 cars will enter the car wash

Solution

The poison formular is given as

`P(X=x)=(e^(-\lambda)\lambda^x)/(x!)`

Where

`\begin{gathered} e=constant=2.718 \\ \lambda=is\text{ }an\text{ }average\text{ }rate\text{ }of\text{ }the\text{ }expected\text{ }value\text{ }and\text{ }λ=variance,alsoλ>0 \end{gathered}`

If we have a mean rate of 3 cars per half an hour. Therefore in an hour the mean rate would be 6

So, substituting into the formula

`P(X=4)=(2.718^(-6)*6^4)/(4!)=`
`\begin{gathered} =(1296)/(403.178*24) \\ =0.13393 \\ x\approx0.1339(4decimal-place) \end{gathered}`

Hence, the probability is approximately 0.1339