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Question

For women's collegiate competition, a basketball's circumference, mass, and bounce height must fall within given tolerance levels of regulation measurements. The table shows these tolerance levels äs well as measurements taken on five different basketballs. Which basketball meets all of the specified tolerances? $$ \begin{matrix} \text{ } & \text{Circumference (mm)} & \text{Mass (g)} & \text{Bounce Height (mm)}\\ \text{Tolerance} & {730.56 \pm 6.5} & {53.8.5 \pm 48.5} & {1358.5 \pm 63.5}\\ \text{Basketball #1} & \text{729.8} & \text{509.3} & \text{1343.4}\\ \text{Basketball #2} & \text{723.5} & \text{529.8} & \text{1299.8}\\ \text{Basketball #3} & \text{734.2} & \text{542.6} & \text{1293.5}\\ \text{Basketball #4} & \text{725.5} & \text{528} & \text{1364.5}\\ \text{Basketball #5} & \text{740} & \text{555.9} & \text{1407.4}\\ \end{matrix} $$

Solution

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Answered 2 years ago
Answered 2 years ago
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Firstly, we should find the range of given values.

Circumference(mm)=730.56±6.5=730.56+6.5,730.56.5=737.06,724.06Mass(g)=538.5±28.5=538.5+28.5,538.528.5=567,510Bounce Height(mm)=1358.5±63.5=1358.5+63.5,1358.563.5=1422,1295\begin{aligned} \text{Circumference(mm)} &= 730.56\pm6.5\\ &=730.56 + 6.5, 730.5 - 6.5\\ &= 737.06, 724.06\\ \text{Mass(g)} &= 538.5\pm28.5\\ &= 538.5 + 28.5, 538.5 - 28.5\\ &= 567, 510\\ \text{Bounce Height(mm)} &=1358.5\pm63.5\\ &= 1358.5 +63.5, 1358.5 -63.5\\ &= 1422,1295\\ \end{aligned}

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