Question 7
In a normal distribution, which of the following statements is true about the area that falls between one standard
deviation above and one standard deviation below the mean?
(A
It contains the bottom 50% of the distribution.
B
It contains the middle 50% of the distribution.
©
It contains the bottom 68% of the distribution.
0
It contains the middle 68% of the distribution
E
It is the same as the square of the average deviation
ER
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Answer:

Using the Empirical Rule, the correct option is given by:

It contains the middle 68% of the distribution.

Explanation:

Lanuel

By using the Empirical Rule, the statement which is true about the area in a normal distribution is: D. it contains the middle 68% of the distribution.

What is the empirical rule?

The empirical rule is also referred to as the 68-95-99.7 rule or three-sigma rule and it can be defined as a statistical rule which states that:

  • The middle 68% of a normal distribution would be within one standard deviation of its mean.
  • The middle 95% of a normal distribution would be within two standard deviations of its mean.
  • The middle 99.7% of a normal distribution would be within three standard deviations of its mean.

In conclusion, the statement which is true about the area that falls between one (1) standard deviation above and one (1) standard deviation below the mean in a normal distribution is that it contains the middle 68% of the distribution.

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