Final answer:
To find the probability of 18 customers arriving within the next hour at your bank, you can use the Poisson distribution. The average number of customers arriving per minute is 0.5. Substitute the values into the Poisson distribution formula to calculate the probability and convert it to a percentage.
Step-by-step explanation:
To find the probability of 18 customers arriving within the next hour at your bank, you can use the Poisson distribution. The Poisson distribution is used to model the number of events occurring in a fixed interval of time or space. In this case, the average number of customers arriving per hour is given as 30, so the average number of customers arriving per minute is 0.5 (30 divided by 60).
The formula for the Poisson distribution is:
- P(x) = (e^(-λ) * λ^x) / x!
where P(x) is the probability of x events occurring, λ is the average number of events occurring in the given interval, and x is the number of events.
In this case, we want to find the probability of 18 customers arriving within the next hour, which is equivalent to the probability of 0.5 customers arriving every minute.
So, substituting the values into the formula:
- P(18) = (e^(-0.5) * 0.5^18) / 18!
Calculating this probability will give you the answer in decimal form. To convert it to a percentage, simply multiply it by 100.