When using the beta distribution,the denominator of the formula for standard deviation should ________.
A)be approximately one-sixth of its range.
B)be adjusted by converting the range into the correct statistical variance
C)be adjusted by converting the range into the correct z-score value
D)be adjusted by converting the range into 50 percent of the mean

Question

Quizplus · Accepted Answer

The standard deviation of a beta distribution is given by a formula that involves its range and ratio parameters. Specifically, the formula is SD = sqrt[(range * (1 - range)) / (1 + alpha + beta)], where alpha and beta are the ratio parameters. The denominator of this formula should be approximately one-sixth of the range, which means that as the range becomes larger, so too should the denominator. This is because a larger range implies greater variability, which requires a larger denominator to accommodate for this variability. Therefore, choice A is the correct answer. The other choices are incorrect because they either involve converting the range into an arbitrary value or into a different statistical measure altogether (variance or z-score).

When Using the Beta Distribution,the Denominator of the Formula for Standard