Which statement is true of normally distributed data?

A.
Approximately 90% of data falls within 2 standard deviations (±2) of the mean.

B.
Approximately 90% of data falls within 3 standard deviations of (±3) the mean.

C.
Approximately 95% of data falls within 2 standard deviations (±2) of the mean.

D.
Approximately 95% of data falls within 3 standard deviations (±3) of the mean.

Please explain and no answering just for points.

C

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Approximately 95% of data falls within 2 standard deviations (±2) of the mean. Option D is correct.

A normal distribution is a type of continuous probability distribution for a real-valued random variable such that the values are symmetric about a mean and the curve has bell shape.

Standard deviation is the measure of the randomness of the distribution. The curve has its peak at the mean.

As standard deviation increases, the peak of the curve comes lower and the distribution becomes more and more dispersed.

In a normal distribution 68% of the values falls within 1 standard deviation

and 95% of the values falls within two standard deviations. 99% of the values falls within three standard deviations.

Hence, approximately 95% of data falls within 2 standard deviations (±2) of the mean.

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