# 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?

Oct 28, 2015

$= 1 - \Phi \left(\frac{2}{3}\right)$

#### Explanation:

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

Note that our required probability is

$P \left[X > 110\right] = 1 - P \left[X \le 110\right]$
$= 1 - P \left[\frac{X - 100}{15} \le \frac{110 - 100}{15}\right]$
$= 1 - \Phi \left(\frac{2}{3}\right)$

Note that $\Phi \left(x\right)$ is the cumulative density function of standard normal distribution .