For a normal distribution with μ = 75 and Q = 5, what score (X)

Question

what score (X) separates the bottom 33% from the rest of the distribution?

Answer 1

Hi Bryana, if you look at a normal distribution table, 33 percent or .33 is found at -.44. To calculate the dividing line, use the following:

Z-score = (Missing value - mean) / standard deviation

Here the Z-score is -0.44.

The mean is 75 and the standard deviation is 5.

Substitute to find the missing value, we call x:

-0.44 = (x - 75) / 5

x = 5 * -0.44 + 75

x = 72.8

The score that separates the bottom 33 % from the rest is 72.8.

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