1. ## [SOLVED] Normal Distribution

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?

2. hi

For normal distribution:

$P(X\leq x)=\Phi\left(\frac{x-\mu}{\sigma}\right)$

For 10% to be higher, we need $P(x\leq x)=0.9$

Therefore...

$0.9=\Phi\left(\frac{x-1.5}{1}\right)$

Looking at the standard distribution table, we see that $0.9$ corresponds to approx. $1.28$

In other words, solve $\frac{x-1.5}{1}=1.28$

Gives $x = 2.78$

So the loan is 2,780,000(czk)

3. Thanks Twig