During lunch hour, customers arrive at a fast food drive-through window, on average, every 3.8 minutes. Assume arrival time follows the exponential probability distribution. a) What is the probability that the next customer will arrive within the next 3 minutes? b) What is the probability that the next customer will arrive in more than 7 minutes? c) What is the probability that the next customer will arrive between 1 and 6 minutes?

a) 54.68% probability that the next customer will arrive within the next 3 minutes

b) 15.78% probability that the next customer will arrive in more than 7 minutes

c) 56.27% probability that the next customer will arrive between 1 and 6 minutes

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

In which is the decay parameter.

The probability that x is lower or equal to a is given by:

Which has the following solution:

During lunch hour, customers arrive at a fast food drive-through window, on average, every 3.8 minutes.

This means that

a) What is the probability that the next customer will arrive within the next 3 minutes?

54.68% probability that the next customer will arrive within the next 3 minutes

b) What is the probability that the next customer will arrive in more than 7 minutes?

Either it will arrive in 7 minutes or less, or it will arrive in more than 7 minutes. The sum of the probabilities of these outcomes is decimal 1. So

We want P(X > 7). So

15.78% probability that the next customer will arrive in more than 7 minutes

c) What is the probability that the next customer will arrive between 1 and 6 minutes?

56.27% probability that the next customer will arrive between 1 and 6 minutes

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step-by-step explanation: