A McDonald’s manager knows that cars arrive at the drive-through at the average rate of two cars per minute between the hours of 12 noon and 1:00 p.m.

Determine and interpret the probability of the following events:

(a) Exactly six cars arrive between 12 noon and 12:05 p.m.

(b) Fewer than six cars arrive between 12 noon and 12:05 p.m.

(c) At least six cars arrive between 12 noon and 12:05 p.m.

Approach The cars arrive at a rate of two per minute over the time interval between 12 noon and 1:00 p.m. The random variable X follows a Poisson process, where x = 0, 1, 2, . . . . The Poisson probability distribution function requires a value for λ and t. Since the cars arrive at a rate of two per minute, λ = 2.

The interval of time we are interested in is five minutes, so t = 5. Use the Poisson probability distribution function (1).

Data from distribution function (1).

Transcribed Image Text:

(At)* P(x) = e- x! x = 0, 1, 2, 3,... (1)