Hi, there--

Problem:
The grades on certain statistics tests are normally distributed with a mean of 76 and a 
standard deviation of 8. Find the probability that a randomly chosen score from this test is 
less than or equal to 72.

Solution:
First, we find the z-score which allows us to compare this normal curve with the standard 
normal curve. We have
mean = μ = 76
standard deviation = σ=8
randomly chosen score = x = 72

We want to know P (x≤72).

z = (x -μ)/σ = (72-76)/8 = -0.5

Most z-tables will have a shaded picture of a normal curve which tells you how to interpret 
the z-vales,

P (x≤72) = P(z≤-0.5) = 0.3085

The probability of getting a score less than or equal to 76 is 0.3085.

~Mrs.Figgy