Which of the following are true of a normal distribution?
I. A larger standard deviation gives a flatter, wider curve.
II. The curve is highest at the mean.
III. The curve is skewed to the right.
IV. The probability that $X$ equals one exact value is 0.

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

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

I: the total area stays 1, so a wider spread means a lower peak. II: the peak is at the mean. IV: a single point has no width, so no area.
III is false: the normal curve is symmetric, not skewed.

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

The rule this testsThe normal curve

Practise this chapter →

Ten questions from Normal Distribution, at your own pace.

Which of the following are true of a normal distribution?I. A larger standard deviation gives a flatter, wider curve.II. The curve is highest at the mean.III. The curve is skewed to the right.IV. The probability that XXX equals one exact value is 0.

Explanation

Which of the following are true of a normal distribution?
I. A larger standard deviation gives a flatter, wider curve.
II. The curve is highest at the mean.
III. The curve is skewed to the right.
IV. The probability that $X$ equals one exact value is 0.