Which of the following describes the distinguishing properties of a normal distr

Question

Which of the following describes the distinguishing properties of a normal distribution?

Select one:

a.

Its middle 50% is within 1.33 standard deviations of its mean

b.

Its measures of central tendency are all equal

c.

99.7% of its values are contained within three standard deviations of its mean

d. All of the above

How can you use the normal probability plot to evaluate whether a set of data is normally distributed?

Select one:

a.

If the distribution is normal, the plot of the Z values on the horizontal axis and the original values on the vertical axis will be a bell curve.

b.

If the distribution is normal, the plot of the Z values on the horizontal axis and the original values on the vertical axis will be a straight line.

c.

If the distribution is normal, the plot of the standard deviation on the horizontal axis and the original values on the vertical axis will be a straight line.

Explanation / Answer

Note: In normal diatribution,

Mean = Median = Mode

That is measures of central tendency are equal.

Q.1) Amswer: b)

In normal distribution, Its measures of central tendency are all equal

Q.2) Answer:

b) If the distribution is normal, the plot of the Z values on the horizontal axis and the original values on the vertical axis will be a straight line.

Note: Steps for constructing normal probability plot:

1. arrange data into an ordered array
2. find corresponding standardized normal quantile values (z)
3. plot the pairs of points with observed data values (x) on the vertical axis and the standardized normal quantile values (Z) on the horizontal axis
4. evaluate the plot for evidence for linearity

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