Question

For a normal distribution with a mean of m = 80 and a standard deviation of s = 20, find the proportion of the population corresponding to each of the following scores.

a. Scores greater than 85
b. Scores less than 100
c. Scores between 70 and 90

I believe this is the correct formula to start with but am unclear on how to finish it. Any help would be appreciated.

a. z = X-m= 85–80 = 5 = 0.25
s 20 20

b. z = X-m= 100–80 = 20 = 1.00
s 20 20

c. z = X-m= 70–80 = -10 = -0.25
s 20 20
z = X-m= 90–80 = 10 = 0.50
s 20 20

Answer 1

What does "s 20 20" mean?

Z = (x-mean)/SD

Type equation completely to avoid mistakes.

c. -10/20 = ?

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportions related to the Z scores you have found.

I hope this helps.