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Chapter 9: Problem 480
Find the midrange of this sample of SAT-Verbal scores. The sample had the smallest observation of 426 and the largest at 740 .
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The results of a survey show that the 518 respondents may be categorized as 0 0 Protestant - Republicans Protestant - Democrats Protestant - Independents Catholic - Republicans Catholic - Democrats Catholic-Independents Jewish - Republicans Jewish - Democrat Jewish - Independents \begin{tabular}{c} 126 \\ 71 \\ 19 \\ 61 \\ 93 \\ 14 \\ 38 \\ 69 \\ 27 \\ \hline \end{tabular} 38 6 Given this data construct a contingency table.
Find \(\mathrm{E}(\mathrm{X})\) for the continuous random variables with
probability density functions;
a) \(f(x)=2 x, 0
Find the expected value and variance of a random variable, $$ \mathrm{Y}=\mathrm{a}_{1} \mathrm{X}_{1}+\mathrm{a}_{2} \mathrm{X}_{2}+\ldots \ldots+\mathrm{a}_{\mathrm{n}} \mathrm{X}_{\mathrm{n}} $$ where the \(\mathrm{X}_{\mathrm{i}}\) are independent and each have mean \(\mu\) and variance \(\sigma^{2}\). The \(a_{i}\) are constants.
A highly specialized industry builds one device each month. The total monthly demand is a random variable with the following distribution. $$ \begin{array}{|l|l|l|l|l|} \hline \text { Demand } & 0 & 1 & 2 & 3 \\ \hline \mathrm{P}(\mathrm{D}) & 1 / 9 & 6 / 9 & 1 / 9 & 1 / 9 \\ \hline \end{array} $$ When the inventory level reaches 3, production is stopped until the inventory drops to 2 . Let the states of the system be the inventory level. The transition matrix is found to be \(\begin{array}{rlllll} & & 0 & 1 & 2 & 3 \mid \\\ & 0 & 8 / 9 & 1 / 9 & 0 & 0 \\ & 11 & 2 / 9 & 6 / 9 & 1 / 9 & 0 \\\ \mathrm{P}= & 12 & 1 / 9 & 1 / 9 & 6 / 9 & 1 / 9 \\ & 13 & 1 / 9 & 1 / 9 & 6 / 9 & 1 / 9\end{array}\) Assuming the industry starts with zero inventory find the transition matrix as \(\mathrm{n} \rightarrow \infty\)
In investigating several complaints concerning the weight of the "NET WT. 12 OZ." jar of a local brand of peanut butter, the Better Business Bureau selected a sample of 36 jars. The sample showed an average net weight of \(11.92\) ounces and a standard deviation of \(.3\) ounce. Using a \(.01\) level of significance, what would the Bureau conclude about the operation of the local firm?
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