Answer:
0.9595724
Step-by-step explanation:
Time taken to wash a car (μ) = 5 minutes
Hence, Number of cars washed per hour = 60/5 = 12 cars
If 5 cars arrive, 30 minutes to closing ; it takes 25 minutes to finish up ;
If 1 more car arrives, then it takes exactly 30 minutes
Hence, there will be no one in line at closing ;
IF 0 or 1 car arrives, if more than 1 car arrives, then there will be people in line at closing.
Hence, probability of waiting in line at closing :
1 - [p(0) + p(1)]
Using poisson :
P(x) = [(e^-μ) * (μ^x)] / x!
If x = 0
P(0) = [(e^-5) * (5^0)] / 0!
P(0) = (0.0067379 * 1) / 1
P(0) = 0.0067379
X = 1
P(1) = [(e^-5) * (5^1)] / 1!
P(0) = (0.0067379 * 5) / 1
P(0) = 0.0336897
Hence,
1 - (0.0067379 + 0.0336897)
1 - 0.0404276
= 0.9595724
Hence, the probability that anyone would be in the car washing line after closing is 0.9595724
