Standard Normal DistributionA random variable X is normally distributed with a mean (µ) of 80 and standard deviation (σ) of 10. If the z-score of a point on X is -1.5, then what is the value of that point on X?65957293
Question
Standard Normal DistributionA random variable X is normally distributed with a mean (µ) of 80 and standard deviation (σ) of 10. If the z-score of a point on X is -1.5, then what is the value of that point on X?65957293
Solution
The z-score is a measure of how many standard deviations an element is from the mean. In this case, a z-score of -1.5 means the value is 1.5 standard deviations below the mean.
The formula to calculate the value from a z-score is:
X = µ + Zσ
Where: X is the value we want to find, µ is the mean, Z is the z-score, and σ is the standard deviation.
Substituting the given values into the formula:
X = 80 + (-1.5 * 10) X = 80 - 15 X = 65
So, the value of the point on X that corresponds to a z-score of -1.5 is 65.
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