QUESTION 4 The following table shows the distribution of the price for a dwelling sold in a certain city during necember 2021. \begin{tabular}{|l|l|l|l|l|l|} \hline Price of dwelling (in R1000) & \multicolumn{1}{|c|}{ Number sold \( f \)} & Cumulative Frequency \( (F) \) & Middle valuc \( \left(x_{i}\right) \) & \( f_{i} \) & \( x_{i}^{\prime} \) \\ \hline\( [70 ; 75) \) & 55 & 55 & & & \\ \hline\( [75 ; 80) \) & 80 & 135 & & \\ \hline\( [80 ; 85) \) & 110 & 245 & & \\ \hline\( [85 ; 90) \) & 240 & 485 & & \\ \hline\( [90 ; 95) \) & 125 & 610 & & \\ \hline\( [95 ; 100) \) & 70 & 680 & & \\ \hline\( [100 ; 105) \) & 50 & 730 & & \\ \hline\( [105 ; 110) \) & 40 & 770 & & \\ \hline\( [110 ; 115) \) & 30 & 800 & & \\ \hline Total & 800 & & & \\ \hline \end{tabular} 4.1 Complete TABLE 2.1 4.2 Calculate the arithmetic mean \( (\bar{x}) \)
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The following table shows the average percentage increase in the price of a house from 1980 to 2001 in nine regions of the United States: ${ }^{7}$ $$ \begin{array}{|l|c|} \hline \text { Region } & \text { Percent Increase } \\ \hline \text { New England } & 300 \\ \hline \text { Pacific } & 225 \\ \hline \text { Middle Atlantic } & 225 \\ \hline \text { South Atlantic } & 150 \\ \hline \text { Mountain } & 150 \\ \hline \text { West North Central } & 125 \\ \hline \text { West South Central } & 75 \\ \hline \text { East North Central } & 150 \\ \hline \text { East South Central } & 125 \\ \hline \end{array} $$ Let $X$ be the percentage increase in the price of a house in a randomly selected region. a. What are the values of $X ?$ b. Compute the frequency and probability distribution of $X$. [HINT: See Example 5.] c. What is the probability that, in a randomly selected region, the percentage increase in the cost of a house exceeded $200 \% ?$
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Find the mean for the following frequency tables: A. $$\begin{array}{|l|l|} \hline \text { Grade } & \text { Frequency } \\ \hline 49.5-59.5 & 2 \\ \hline 59.5-69.5 & 3 \\ \hline 69.5-79.5 & 8 \\ \hline 79.5-89.5 & 12 \\ \hline 89.5-99.5 & 5 \\ \hline \end{array}$$ B. $$\begin{array}{|l|l|} \hline \text { Daily Low Temperature } & \text { Frequency } \\ \hline 49.5-59.5 & 53 \\ \hline 59.5-69.5 & 32 \\ \hline 69.5-79.5 & 15 \\ \hline 79.5-89.5 & 1 \\ \hline 89.5-99.5 & 0 \\ \hline \end{array}$$ C. $$\begin{array}{|l|l|} \hline \text { Points per Game } & \text { Frequency } \\ \hline 49.5-59.5 & 14 \\ \hline 59.5-69.5 & 32 \\ \hline 69.5-79.5 & 15 \\ \hline 79.5-89.5 & 23 \\ \hline 89.5-99.5 & 2 \\ \hline \end{array}$$
The following table shows the average percentage increase in the price of a house from 1980 to 2001 in nine regions of the United States. Let $X$ be the percentage increase in the price of a house in a randomly selected region. a. What are the values of $X$ ? b. Compute the frequency and probability distribution of $X$. c. What is the probability that, in a randomly selected region, the percentage increase in the cost of a house exceeded $200 \%$ ?
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