What is the z-score for x = 85 if the distribution has mean μ = 100 and standard deviation σ = 10?

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Multiple Choice

What is the z-score for x = 85 if the distribution has mean μ = 100 and standard deviation σ = 10?

Explanation:
Z-score shows how many standard deviations a value is from the mean, using the formula z = (x − μ)/σ. With x = 85, μ = 100, and σ = 10, you get z = (85 − 100)/10 = −15/10 = −1.5. So 85 lies 1.5 standard deviations below the mean. For quick intuition, a z-score of −1.0 would put x at 90, −0.5 at 95, and −2.0 at 80, which helps confirm the result.

Z-score shows how many standard deviations a value is from the mean, using the formula z = (x − μ)/σ. With x = 85, μ = 100, and σ = 10, you get z = (85 − 100)/10 = −15/10 = −1.5. So 85 lies 1.5 standard deviations below the mean. For quick intuition, a z-score of −1.0 would put x at 90, −0.5 at 95, and −2.0 at 80, which helps confirm the result.

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