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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
