If you have a normal distribution of a random variable x, with a mean of 56 and standard deviation of 8?

Question

What is the probability that x is greater than 64?

a. 0.190
b. 0.159
c. 0.140

How do you figure this out? I'm stuck, and would rather have the formula, then the answer

Answer 1

68% of the normal distribution will fall between mean - one std dev and mean + one std dev. In this case, 68% will fall between 56-8 and 56+8 or between 48 and 64.

The remaining 32% falls outside of that range. But of that 32%, half of it is less than 48 and half is greater than 64. So there is a 16% chance that x is in the group above 64. One of your possible answers is 0.159, or about 16%. If I had used a more exact value of 68.27% in my discussion above instead of rounding to 68% I would have ended up with the 15.9% which is answer b.