Question

On average, 5 customers arrive at the drive-up window of a fast-food restaurant every 4 minutes during the lunch hour. What is the probability that the next customer will arrive within three minutes? (Use an exponential distribution to determine this probability.)

Answer 1

Answer: 0.9765

Step-by-step explanation:

The cumulative distribution function for exponential distribution for random variable x is given by :-

`F(x)=1-e^(-\lambda x)`, where
`\lambda` is the mean of the distribution .

Given : On average, 5 customers arrive at the drive-up window of a fast-food restaurant every 4 minutes during the lunch hour.

Then
`\lambda=(5)/(4)=1.25`

Now, the probability that the next customer will arrive within three minutes :-

`P(x< 3)=1-e^(-1.25 * 3)=0.97648225\approx0.9765`

Hence, the probability that the next customer will arrive within three minutes = 0.9765