Question

Assume that a normal distribution of data has a mean of 12 and a standard deviation of 3. Use the 68-95-99.7 rule to find the percentage of values that lie below 9.

Answer 1

This is a normal distribution question with

P(x < 9.0)=?
The z-score at x = 9.0 is,

z = -1.0
68% of the values are between z = -1 to 1. So, 100-68 = 32% of the values are outside z = -1 to 1.
Half of the probablity of this region will give us P(x < 9.0)
P(x < 9.0) = 32/2 = 16% of values lie below 9
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