Question

questions-4 cars arriving for gasoline at a particular gas station follow a poisson distribution with a mean of 5 per hour. (use excel for this question and submit the excel file). a) determine the probability that over the next hour only one car will arrive. (5 points) b) compute the probability that in the next 3 hours more than 20 cars will arrive. (5 points)

Answer 1

a) The probability of only one car arriving in the next hour is approximately 0.067.

b) The probability of more than 20 cars arriving in the next 3 hours can be found by subtracting the probability of 20 or fewer cars from 1.

Step-by-step explanation:

a) To determine the probability that only one car will arrive in the next hour, we need to use the Poisson distribution formula. The Poisson distribution formula is P(x; μ) = (e^(-μ) * μ^x) / x!, where x is the number of events and μ is the mean. In this case, x = 1 and μ = 5 (since the mean is given as 5 cars per hour). Plugging these values into the formula, we get P(1; 5) = (e^(-5) * 5^1) / 1! ≈ 0.067.

b) To compute the probability that more than 20 cars will arrive in the next 3 hours, we can use the complement rule. First, we find the probability that 20 or fewer cars will arrive in the next 3 hours. Using the Poisson distribution formula with x = 20 and μ = 5 (since the mean is given as 5 cars per hour), we get P(≤20; 15) = ∑(i=0 to 20) (e^(-15) * 15^i) / i!. Then, we subtract this probability from 1 to find the probability of more than 20 cars arriving.