SOLUTION: Because of the relatively high interest rates, most consumers attempt to pay off their credit card bills promptly. However, this is not always possible. An analysis of the amount o
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Question 1179578: Because of the relatively high interest rates, most consumers attempt to pay off their credit card bills promptly. However, this is not always possible. An analysis of the amount of interest paid monthly by a bank's Visa cardholders reveals that the amount is normally distributed with a mean of 27 dollars and a standard deviation of 6 dollars.
What interest payment is exceeded by only 18% of the bank's Visa cardholders?
Interest Payment = Answer by CPhill(1987) (Show Source):
You can put this solution on YOUR website! **1. Find the z-score**
We want to find the z-score that corresponds to the 82nd percentile (100% - 18% = 82%). This is because we're looking for the value that is *exceeded* by only 18%, meaning 82% of the values fall below it.
You can use a z-table or a calculator with a built-in inverse normal function to find this z-score. The z-score corresponding to the 82nd percentile is approximately 0.92.
**2. Use the z-score formula**
The z-score formula is:
z = (X - μ) / σ
Where:
* z = z-score
* X = the value we want to find (the interest payment)
* μ = the mean (27 dollars)
* σ = the standard deviation (6 dollars)
**3. Plug in the values and solve for X**
0.92 = (X - 27) / 6
Multiply both sides by 6:
5.52 = X - 27
Add 27 to both sides:
X = 32.52
**Answer:**
An interest payment of **$32.52** is exceeded by only 18% of the bank's Visa cardholders.
