Question

Cars arriving for gasoline at a shell station follow a Poisson distribution with a mean of 7 per hour. a. Determine the probability that over the next hour, only one car will arrive. b. Compute the probability that in the next 5 hours, more than 4 cars will arrive?

Answer 1

The probability of exactly one car arriving in the next hour at a station with a mean of 7 cars per hour is approximately 0.09%. For the next 5 hours, with a mean of 35 cars, the probability that more than 4 cars will arrive is essentially 1.

Step-by-step explanation:

Cars arriving for gasoline at a Shell station follow a Poisson distribution with a mean of 7 per hour. To solve part a, we use the Poisson probability formula: P(X = x) = (e^-μ * μ^x) / x!. For only one car arriving in the next hour (μ = 7, x = 1), the probability is:

P(1) = (e^-7 * 7^1) / 1! = 0.00091188, or approximately 0.09%.

For part b, since we are interested in the number of cars in the next 5 hours, we adjust our mean to 5 * 7 = 35. The probability of more than 4 cars arriving can be found by subtracting the probabilities of 0, 1, 2, 3, and 4 cars arriving from 1:

P(X > 4) = 1 - [P(0) + P(1) + P(2) + P(3) + P(4)], which is essentially 1 as the mean is significantly higher than 4.