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Range, mean, and variance of the normal probability curve
Question

Range, mean, and variance of the normal probability curve

A.

−∞ to +∞; μ; σ²

B.

−3 to +3; μ; σ²

C.

−∞ to +∞; 0; 1

D.

−3 to +3; 0; 1

Correct option is A

The general normal distribution ranges theoretically from negative to positive infinity, with mean μ and variance σ². (Options C and D describe the standard normal distribution's z-score properties, not the general normal curve's range/mean/variance.)
Information Booster:
1. The normal curve is asymptotic — it never actually touches the x-axis.
2. The standard normal distribution has mean 0 and standard deviation 1 (a special case).
3. About 99.7% of data lies within ±3 SD of the mean (empirical rule).
4. Skewness = 0 and kurtosis = 3 (mesokurtic) for a perfect normal distribution.

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