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The store owner converts the frequency table to a conditional relative frequency table by row.

Beach Towel Sales

\begin{tabular}{|c|c|c|c|}
\cline { 2 - 4 } \multicolumn{1}{c|}{} & Full Price & Discounted & Total \\
\hline Month 1 & 0.98 & 0.02 & 1.0 \\
\hline Month 2 & 0.96 & 0.04 & 1.0 \\
\hline Month 3 & 0.808 & 0.192 & 1.0 \\
\hline Total & [tex][tex]$X$[/tex][/tex] & [tex][tex]$Y$[/tex][/tex] & 1.0 \\
\hline
\end{tabular}

Which value should he use for [tex][tex]$X$[/tex][/tex]? Round to the nearest hundredth.
A. 0.89
B. 0.90
C. 0.92
D. 0.96



Answer :

GinnyAnswer
Sure, let's go through the process to determine the value of [tex]\( X \)[/tex], the total proportion of beach towels sold at full price over three months.

Given the data:
- Month 1: 0.98 (Full Price) + 0.02 (Discounted) = 1.0
- Month 2: 0.96 (Full Price) + 0.04 (Discounted) = 1.0
- Month 3: 0.808 (Full Price) + 0.192 (Discounted) = 1.0

To obtain the average proportion of beach towels sold at full price across these three months, calculate the mean of the full price proportions for each month.

1. First, sum the proportions of beach towels sold at full price for each month:
[tex]\[ 0.98 + 0.96 + 0.808 \][/tex]
2. Now, divide this sum by 3 to find the average:
[tex]\[ \frac{0.98 + 0.96 + 0.808}{3} \][/tex]
3. Sum the numbers:
[tex]\[ 0.98 + 0.96 = 1.94 \\ 1.94 + 0.808 = 2.748 \][/tex]
4. Divide by 3:
[tex]\[ \frac{2.748}{3} = 0.916 \][/tex]
5. Round 0.916 to the nearest hundredth:
[tex]\[ 0.916 \approx 0.92 \][/tex]

Hence, the value the store owner should use for [tex]\( X \)[/tex] is [tex]\( 0.92 \)[/tex]. The correct answer is:
- 0.92

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