A banker finds that the number of times people use automated-teller machines in a year are normally distributed with a mean of 40.0 and a standard deviation of 11.4. What is the percentage of customers who use them less than 25 times?
1 Answer
9.34%.
Explanation:
Since we are told this distribution is normal, we can convert our provided values to a standardized z-score value, and then consult a z-score table to find the requested percentage.
First, note that we have
To find the percentage of customers who use the ATMs less than 25 times, we simply refer to a z-score table and find the z-score we just determined (-1.32) and use the table to find the left-tail area under the normal curve.
Using one table, we see that this corresponds to an area of 0.0934, or roughly 9.34% of all customers.