For X ~ N(μ = 100, σ = 5), what is the z-score for X = 110?

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Multiple Choice

For X ~ N(μ = 100, σ = 5), what is the z-score for X = 110?

Explanation:
The z-score shows how many standard deviations a value is from the mean, using z = (X − μ) / σ. Here, X = 110, μ = 100, and σ = 5, so z = (110 − 100) / 5 = 10 / 5 = 2. This means 110 is two standard deviations above the mean. The other numbers correspond to different X values: a z-score of −2 would come from X = 90, a z-score of 1 from X = 105, and a z-score of 0 from X = 100. So the correct z-score is 2.

The z-score shows how many standard deviations a value is from the mean, using z = (X − μ) / σ. Here, X = 110, μ = 100, and σ = 5, so z = (110 − 100) / 5 = 10 / 5 = 2. This means 110 is two standard deviations above the mean. The other numbers correspond to different X values: a z-score of −2 would come from X = 90, a z-score of 1 from X = 105, and a z-score of 0 from X = 100. So the correct z-score is 2.

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