Question

A normally distributed data has a mean of 200 and a standard deviation of 20.What is the lowest value that belongs to the upper 10% of the distribution?

Answer 1

$$P(X>x)=1-P(Z\le\dfrac{x-\mu}{\sigma})$$

$$=1-P(Z\le\dfrac{x-200}{20})=0.10$$

$$\dfrac{x-200}{20}\approx1.281552$$

$$x=200+20(1.281552)$$

$$x=225.631$$