How many spaces should be provided to have a 96% probability of accommodating all of the waiting cars?
A)10
B)11
C)12
D)13
E)14

Question

Quizplus · Accepted Answer

To determine how many spaces are needed to accommodate all waiting cars with a 96% probability, we can use the Poisson distribution formula. The formula for the Poisson distribution is P(X=x) = (e^-λ * λ^x) / x!, where λ is the average rate of arrivals, and x is the number of arrivals. In this case, λ = 10 (since 10 cars arrive per hour) and we want to find the minimum number of spaces needed to accommodate all waiting cars with a 96% probability.

To solve, we can use trial and error with the cumulative Poisson distribution function, which gives us the probability of having x or fewer arrivals. For example, P(X≤12) = Σi=0 to 12 (e^-λ * λ^i) / i! = 0.958.

This means that if we have 12 spaces, there is a 95.8% probability of being able to accommodate all waiting cars. To increase the probability to 96%, we would need to add one more space, making the answer C)12.

How Many Spaces Should Be Provided to Have a 96