Answer:
The probability that five cars will arrive during the next thirty minute interval is 0.0127.
Step-by-step explanation:
Let X = number of cars arriving at Sami Schmitt's Scrub and Shine Car Wash.
The average number of cars arriving in 20 minutes is, 8.
The average number of cars arriving in 1 minute is, [tex]\frac{8}{20}=\frac{2}{5}[/tex].
The average number of cars arriving in 30 minutes is, [tex]\frac{2}{5}\times 30=12[/tex].
The random variable X follows a Poisson distribution with parameter λ = 12.
The probability mass function of X is:
[tex]P(X=x)=\frac{e^{-12}12^{x}}{x!};\ x=0,1,2,3...[/tex]
Compute the probability that 5 cars will arrive in 30 minutes as follows:
[tex]P(X=5)=\frac{e^{-12}12^{5}}{5!}[/tex]
[tex]=\frac{6.1442\times10^{-6}\times 48832}{120}[/tex]
[tex]=0.0127[/tex]
Thus, the probability that five cars will arrive during the next thirty minute interval is 0.0127.
