Answer:
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