ATM transaction times are normally distributed with a mean of 150 seconds and a standard deviation of 45 seconds. What is the probability a person takes less than 60 seconds to complete their transaction?
http://davidmlane.com/hyperstat/z_table.html
THX Damon
You are welcome.
To find the probability that a person takes less than 60 seconds to complete their transaction, we need to calculate the area under the normal distribution curve to the left of 60 seconds.
First, we need to standardize the value. We can do this by subtracting the mean from 60 and then dividing by the standard deviation:
Standardized value = (60 - 150) / 45 = -90 / 45 = -2
Now, we look up the z-score corresponding to this standardized value. We can use a standard normal distribution table or a calculator to find the cumulative probability (also known as the z-score) for the standardized value of -2.
Using a standard normal distribution table or a calculator, we find that the cumulative probability for a z-score of -2 is approximately 0.0228.
Therefore, the probability that a person takes less than 60 seconds to complete their transaction is approximately 0.0228, or 2.28%.