Question

On average, the number of customers who had items to return for refunds or exchanges at a certain retail store's service desk is 756 per week. Find the probability that the service desk will have at least 100 customers with returns or exchanges on a randomly selected day. (Assume the store is open 7 days/week.)

Answer 1

Answer:

The probability that the service desk will have at least 100 customers with returns or exchanges on a randomly selected day is P=0.78.

Step-by-step explanation:

With the weekly average we can estimate the daily average for customers, assuming 7 days a week:

$M=756/7=108$

We can model this situation with a Poisson distribution, with parameter λ=108. But because the number of events is large, we use the normal aproximation:

$P(\lambda)\approx N(\lambda,\lambda)$

Then we can calculate the z value for x=100:

$z=\frac{x-\mu}{\sigma}=\frac{100-108}{\sqrt{108}}=\frac{-8}{10.4} =-0.77$

Now we calculate the probability of x>100 as:

$P(x>100)=P(z>-0.77)=0.78$

The probability that the service desk will have at least 100 customers with returns or exchanges on a randomly selected day is P=0.78.