A bank loan officer rates applicates for credit. The rating are normally distributed with a mean of 200 and a standard deviation of 50. Find the P60, the score which separates the lower 60% from the top 40%.
I get 212.7, using the normal distribution tool at http://psych.colorado.edu/~mcclella/java/normal/accurateNormal.html
Enter the mean and the std dev. and a "start" value of 0. Then try different "end" values like 210 and hit "enter" and see what the probability is for being in that range. Keep chaning the "end" value until you get a probability of 0.600
Those are pretty low credit scores! No wonder the banks are in trouble!
To find the P60, the score which separates the lower 60% from the top 40%, you can use the cumulative distribution function (CDF) of the normal distribution.
First, you need to calculate the z-score corresponding to the desired percentile. The z-score represents the number of standard deviations a particular value is from the mean. In this case, we want to find the z-score that corresponds to the lower 60% of the distribution.
The formula to convert a given percentile to a z-score is:
z = invNorm(percentile, mean, standard deviation)
where invNorm is the inverse of the standard normal distribution function, which can be found in statistical software or using online calculators.
To find the P60 or the score that separates the lower 60% from the top 40%, we need to find the z-score such that the cumulative probability up to that z-score is 0.60.
Using the z-score formula, we have:
z = invNorm(0.60, 200, 50)
By applying the formula, we find that the z-score is approximately 0.253.
After obtaining the z-score, we can find the P60 score by using:
P60 = mean + (z-score * standard deviation)
Substituting the values, we have:
P60 = 200 + (0.253 * 50)
P60 ≈ 212.7
Therefore, the P60 score, which separates the lower 60% from the top 40%, is approximately 212.7.
Please note that the online calculator you mentioned is a useful tool for obtaining the result. However, it's important to understand the underlying calculations and concepts involved.