A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50 . Find $P _ { 60 } ,$ the score which separates the lower 60% from the top 40% .

Question

A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50 . Find $P _ { 60 } ,$ the score which separates the lower  60%  from the top  40% .

Quizplus · Accepted Answer

To find $P_{60}$, the score that separates the lower 60% from the top 40%, we use the Z-score formula and look up the Z value that corresponds to 0.60 in the standard normal distribution table. The Z value for 0.60 is approximately 0.25. Using the Z-score formula $Z = \frac{X - \mu}{\sigma}$, where $X$ is the score, $\mu = 200$ is the mean, and $\sigma = 50$ is the standard deviation, we solve for $X$: $0.25 = \frac{X - 200}{50}$. Solving for $X$ gives $X = 0.25 \times 50 + 200 = 12.5 + 200 = 212.5$.

A Bank's Loan Officer Rates Applicants for Credit P60,P _ { 60 } ,P60​,

A Bank's Loan Officer Rates Applicants for Credit $P _ { 60 } ,$