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

Oct 13, 2015

The probability is about 0.25=25%.

#### Explanation:

If you want to use a standard normal table, take $x = 110$ and convert it to a $z$-score:

$z = \frac{x - \mu}{\sigma} = \frac{110 - 100}{15} = \frac{10}{15} = \frac{2}{3} = 0.666 \ldots \approx 0.67$

Next, use a standard normal table to say:

P(X>110) = P(Z> 0.67) approx 0.25=25%

You might also be able to use your calculator to confirm this without converting to a $z$-score.