Question

A normal distribution is N(u, 16). For X = 52, Z-score is 1, then find the mean
of distribution.
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Answer 1

Answer:

Suppose X ~ N(5, 6). This says that X is a normally distributed random variable with mean μ = 5 and standard deviation σ = 6. Suppose x = 17. Then:

z=\frac{x-\mu }{\sigma }=\frac{17-5}{6}=2

This means that x = 17 is two standard deviations (2σ) above or to the right of the mean μ = 5.

Now suppose x = 1. Then: z = \frac{x-\mu }{\sigma } = \frac{1-5}{6} = –0.67 (rounded to two decimal places)

This means that x = 1 is 0.67 standard deviations (–0.67σ) below or to the left of the mean μ = 5.