Question

If data with a normal distribution has a mean of 100 and a standard deviation of 15, what is the probability that a given value is greater than 110?

Answer 1

`=1- Phi(2/3)`

Explanation:

So here `X ~ N(100, 15^2)`

Note that our required probability is

`P[X>110]= 1-P[X le 110]`
`=1-P[(X-100)/(15) le (110-100)/(15)]`
`=1- Phi(2/3)`

Note that `Phi(x)` is the cumulative density function of standard normal distribution .