Question

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?

Answer 1

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=(x-mu)/sigma=(110-100)/15=10/15=2/3=0.666... 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.