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

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 $\lambda=\dfrac{5}{4}=1.25$

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

$P(x< 3)=1-e^{-1.25 \times 3}=0.97648225\approx0.9765$

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