Loans provided to customers of bank X follows Normal distribution with a mean of 1,500,000 crowns (czk). Given that the standard deviation is 1,000,000 czk which loan amount is such that only 10% of the loans have higher balance?
Loans provided to customers of bank X follows Normal distribution with a mean of 1,500,000 crowns (czk). Given that the standard deviation is 1,000,000 czk which loan amount is such that only 10% of the loans have higher balance?
hi
For normal distribution:
$\displaystyle P(X\leq x)=\Phi\left(\frac{x-\mu}{\sigma}\right) $
For 10% to be higher, we need $\displaystyle P(x\leq x)=0.9 $
Therefore...
$\displaystyle 0.9=\Phi\left(\frac{x-1.5}{1}\right) $
Looking at the standard distribution table, we see that $\displaystyle 0.9 $ corresponds to approx. $\displaystyle 1.28 $
In other words, solve $\displaystyle \frac{x-1.5}{1}=1.28 $
Gives $\displaystyle x = 2.78 $
So the loan is 2,780,000(czk)