Probability Density Functions Can Be Weighted So That Different Properties

question 37

Multiple Choice

Probability density functions can be weighted so that different properties of the distribution can be enhanced or diminished. For instance, if a set of test scores is to be used in comparing the highest performers in a class, one might want to use a pdf, , in which the probability of finding a certain score, f(x) , is multiplied by that score: . A mean found using the weighted pdf might be called a score-weighted mean. Find the score-weighted mean for an exam for which the probability of finding a score is given by the function . You will need to construct the weighted pdf then use it to find the mean score.

• A) 66.7
• B) 60.0
• C) 50.0
• D) 75.0

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Definitions:

Significance Level

A statistical term that quantifies the probability of rejecting the null hypothesis when it is actually true, typically expressed as a percentage or decimal.

Expected Frequency

The predicted count of occurrences for a particular category or event in a statistical distribution, based on a theoretical probability.

Sample Size

The number of observations or data points that are selected from a larger population for purposes of statistical analysis; essential to the reliability of study results.

Goodness-of-Fit Test

A statistical test used to determine how well observed data fit a specific distribution.