Which of the following are true of a normal distribution?
I. Its mean, median and mode are equal.
II. Its curve never touches the horizontal axis.
III. The area to the left of the mean is 0.5.
IV. Its standard deviation can be negative.

I, II and III onlyCorrect answerYour answerAll four: I, II, III and IVCorrect answerYour answerI and III onlyCorrect answerYour answerII, III and IV onlyCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

Symmetry puts the mean, median and mode together (I) and half the area on each side of the mean (III); the tails only approach the axis (II).
IV is false: a standard deviation measures spread and is never negative.

Concept: Properties of the normal distribution
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsThe normal curve

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Ten questions from Normal Distribution, at your own pace.

Which of the following are true of a normal distribution?I. Its mean, median and mode are equal.II. Its curve never touches the horizontal axis.III. The area to the left of the mean is 0.5.IV. Its standard deviation can be negative.

Explanation

Which of the following are true of a normal distribution?
I. Its mean, median and mode are equal.
II. Its curve never touches the horizontal axis.
III. The area to the left of the mean is 0.5.
IV. Its standard deviation can be negative.