An individual's credit soore is a number calculated based on that person's credit history that helps a lender determine how much he/she should be loaned or what creditlimit should be established for a credit card. An article in the Los Angeles Times gave data which suggested that a beta distribution with parameters $A=150, B=850$, $\alpha=8, \beta=2$ would provide a reasonable approximation to the distribution of American credit scores. [Note:credit scores are integer-valued].a. Let $X$ represent a randomly selected American credit score. What are the mean value and standard deviationof this random variable? What is the probability that $X$ is within 1 standard deviation of its mean value?b. What is the approximate probability that a randomly selected score will exceed 750 (which lenders consider a very good score)?
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
An individual's credit soore is a number calculated based on that person's credit history that helps a lender determine how much he/she should be loaned or what credit
limit should be established for a credit card. An article in the Los Angeles Times gave data which suggested that a beta distribution with parameters $A=150, B=850$, $\alpha=8, \beta=2$ would provide a reasonable approximation to the distribution of American credit scores. [Note:
credit scores are integer-valued].
a. Let $X$ represent a randomly selected American credit score. What are the
of this random variable? What is the
b. What is the approximate probability that a randomly selected score will exceed 750 (which lenders consider a very good score)?
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