Suppose X∼N(16.5,2) , and x=18.5 . Find and interpret the z -score of the standardized normal random variable.
Question
Suppose X∼N(16.5,2) , and x=18.5 . Find and interpret the z -score of the standardized normal random variable.
Solution
The z-score is a measure of how many standard deviations an element is from the mean. To calculate the z-score, we use the formula:
z = (x - μ) / σ
where:
- x is the element
- μ is the mean
- σ is the standard deviation
In this case, we have:
- x = 18.5
- μ = 16.5
- σ = 2
Substituting these values into the formula, we get:
z = (18.5 - 16.5) / 2 = 1
So, the z-score of the standardized normal random variable is 1. This means that the value 18.5 is one standard deviation above the mean.
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