Question

The mean of a normally distributed dataset is 12, and the standard deviation is 2.

Answer 1

In the Normal distribution: if the mean (M) is 12 and the standard deviation (s)is 2, then between 8 (12- 2*2, or M - 2 s) and 16 (12 + 2*2, or M+2 s ),or between M - 2 s and M + 2 s lies 13.6 %+ 34.1% + 34.1 % + 13.6% = 95.4% data points. Graph is in the attachment.   

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Answer 2

The correct answer is:

95%

Explanation:

The empirical rule states that 68% of normally distributed data lie within 1 standard deviation of the mean; 95% lie within 2 standard deviations of the mean; and 99.7% lie within 3 standard deviations of the mean.

The mean is 12 and the standard deviation is 2. This means that values from 10 to 14 (12-2, 12+2) are within 1 standard deviation of the mean.

Values from 8 to 16 (12-2-2, 12+2+2) are within 2 standard deviations of the mean. These are the values in question; this means that 95% of the data lie within this range.