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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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Step 1
1 of 3

Firstly, we should find the range of given values.

\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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