Let's say that your average monthly charge is normally distributed with a mean of $500 and a standard deviation of $100. The credit card company will call anytime your purchases for the month exceed the 99th percentile. What is the dollar amount beyond which you will get a call from the credit card company?
http://davidmlane.com/hyperstat/z_table.html
To find the dollar amount beyond which you will get a call from the credit card company, we need to determine the value corresponding to the 99th percentile of the normal distribution.
1. Convert the given mean and standard deviation to the corresponding Z-scores:
Z = (X - mean) / standard deviation
For the 99th percentile, we need to find the Z-score that corresponds to a cumulative probability of 0.99.
2. Look up the Z-score in a standard normal distribution table or use a statistical calculator to find the corresponding value.
The Z-score corresponding to a cumulative probability of 0.99 is approximately 2.33.
3. Use the Z-score formula to solve for the dollar amount beyond which you will get a call from the credit card company:
X = (Z * standard deviation) + mean
X = (2.33 * 100) + 500
X = 233 + 500
X = $733
Therefore, any monthly charge exceeding $733 will result in the credit card company calling you.