Question

which of the following statements accurately describe the characteristics of a normal distribution? select all that are true.
1/8
select all correct options
the curve has inflection points located about one standard deviation from the mean.
the distribution is skewed and has multiple peaks.
the distribution is symmetric and has a single peak unimodal.
approximately 68% of values lie within one standard deviation of the mean, 95% within two, and 99.7% within three.
the mean, median, and mode are equal in value.

Explanation:

• A normal distribution is symmetric and unimodal (single peak).
• Its inflection points lie at $\mu \pm \sigma$, one standard deviation from the mean.
• The empirical rule states ~68% of data is within $\mu \pm \sigma$, ~95% within $\mu \pm 2\sigma$, ~99.7% within $\mu \pm 3\sigma$.
• In a normal distribution, mean, median, and mode are equal.
• It is not skewed and does not have multiple peaks.

Answer:

• The curve has inflection points located about one standard deviation from the mean.
• The distribution is symmetric and has a single peak (unimodal).
• Approximately 68% of values lie within one standard deviation of the mean, 95% within two, and 99.7% within three.
• The mean, median, and mode are equal in value.