Question

Calculate one of each of the following questions created by 3 different classmates


a. Mean and standard deviation given , looking for the percentage between two x values

b. Mean and standard deviation given , looking for the percentage above a certain x value

c. Mean and standard deviation given , looking for the x value at a certain percentile

Answer 1

a) let the two values of x be x1 and x2

P(x1<x<x2)

=$\Phi(\frac {x_2-\mu}{\sigma})-\Phi(\frac {x_1-\mu}{\sigma})$

b)P(X>x)

=$1-\Phi(\frac {x-\mu}{\sigma})$

c) we find $z=\Phi^{-1}(percentile)$

$x=z\sigma+\mu$