Help. Probability statistic? Normal distribution

Given a normal curve w/ m=116.2 and sd=20.
Find. Area bet. 100 and 111.5

Calculate the z-scores

z = x - mean / std

where x is some data value


z_1 = 100 - 116.2 / 20

z_1 = -0.81

Now calculate the other z-score

z_2 = 111.5 - 116.2 / 20

z_2 = -0.235


So with the z-scores we have

P(100 < x < 111.5) = P(-0.81 < x < -0.235)

Step 2: Find P(-0.81 < x < -0.235) with a standard normal table or a calculator


P(-0.81 < x < -0.235) = P(-0.235) - P(-0.81)

≈ P(-0.24) - P(-0.81)

≈ .4052 - .2090

= 0.1962

Solution: Area between 100 and 111.5 is 0.1962.

I rounded to z-score from -0.235 to -0.24.