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question 135

Multiple Choice

Solve the problem.
-The accompanying table shows the probability distribution for x, the number that shows up when a loaded die is rolled. Find the variance for the probability distribution. xP(x) 10.1620.1930.2240.2150.1260.10\begin{array} { c | c } \mathrm { x } & \mathrm { P } ( \mathrm { x } ) \\\hline 1 & 0.16 \\\hline 2 & 0.19 \\\hline 3 & 0.22 \\\hline 4 & 0.21 \\\hline 5 & 0.12 \\\hline 6 & 0.10\end{array}

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Definitions:

Z-test

A statistical test used to determine whether there is a significant difference between the mean of a sample and the population mean, assuming the distribution is normal.

µ = 22

Represents a population mean of 22 in statistical notation.

Null Hypothesis

A hypothesis that there is no effect or no difference, and it is the statement that researchers aim to test against.

Z-statistic

A measure that quantifies the difference between the observed value and the expected value under the null hypothesis, expressed in terms of standard deviations.

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