Suppose X ~ N(5, 6). Suppose x = 12. Calculate the value of Z (2 marks). Z = (x-µ)/σ
Question
Suppose X ~ N(5, 6). Suppose x = 12. Calculate the value of Z (2 marks). Z = (x-µ)/σ
Solution
Sure, let's calculate the Z value step by step.
Step 1: Identify the given values. Here, the mean (µ) is 5, the standard deviation (σ) is the square root of the variance, so σ = sqrt(6), and x = 12.
Step 2: Substitute these values into the Z formula. The Z score formula is Z = (x - µ) / σ.
Step 3: Calculate the Z score. Substituting the given values into the formula, we get Z = (12 - 5) / sqrt(6) = 7 / sqrt(6).
Step 4: Simplify the result. This gives us approximately 2.86.
So, the Z score for x = 12 is approximately 2.86.
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