Question

If µ = 400 and s = 100 the probability of selecting at random a score less than or equal to 370 equals ____.

Answer 1

You'll need to calculate the applicable z-score:
        (given value of x) - (mean value)
z = -----------------------------------------------
                standard deviation

                  370-400            -30
Here, z = ---------------  =  ---------- = -0.3
                      100                100

Use either a table of z scores or your calculator to determine the area under the standard normal curve to the left of z = -0.3.

According to my TI-83 Plus calculator, this area is 0.382.

The probability of selecting at random a score less than or equal to 370 is 0.382.