Question

Type the correct answer in the box. use numerals instead of words. the mean of a normally distributed dataset is 12, and the standard deviation is 2. % of the data points lie between 8 and 16.

Answer 1

The percentage of the data points lying between 8 and 16 will be 95.4%.

What is a normal distribution?

The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.

Type the correct answer in the box. use numerals instead of words. the mean of a normally distributed dataset is 12, and the standard deviation is 2.

Then the percentage of the data points lies between 8 and 16 will be

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.

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Answer 2

The normal distribution is a symmetric probability distribution about the mean. The percentage of values that will be between 8 and 16 is 95.44%.

What is a normal distribution?

The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data distant from the mean. The normal distribution will show as a bell curve on a graph.

Given the mean of the data set is 12, while the standard deviation is 2. Therefore, the percentages of values that will be between 8 and 16 are,

P(8≤x≤16) = P(x≤16) - P(x≤8)

                  $= P(Z\leq \dfrac{16-12}{2}) - P(Z\leq \dfrac{8-12}{2})$

                  = P(Z ≤ 2) - P(Z ≤ -2)

                  =0.9772-0.0228

                  = 0.9544

                  = 95.44%

Hence, the percentage of values that will be between 8 and 16 is 95.44%.

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