Question
Asked Dec 8, 2019
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The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 64 ounces and a standard deviation of 9 ounces.

a) 68% of the widget weights lie between  and 

b) What percentage of the widget weights lie between 37 and 73 ounces?  %

c) What percentage of the widget weights lie below 82 ?  %

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Expert Answer

Step 1

a)

The empirical rule is used find the values. It is given that 68%. This value tells that approximately 68% of the data values lie within one standard deviation from the mean.

By this, the 68% of the widget weights between,

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µ – lo = 64 –9 = 55 µ+lo = 64 +9 = 73 Thus, the 68% of the widget weights between 55 ounces and 73 ounces.

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Step 2

b)

The percentage of the widget weights lie between 37 and 73 ounces is calculated below:

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37— 64 х- и 73—64 P(37 <X <73)= P σ = P(-3<Z<1) = P(Z <1)– P(Z <–3) = 0.8413 – 0.0014 = 0.84 Thus, 84 percent of the widget weights lie between 37 and 73 ounces.

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Step 3

c)

The percentage of the widget weights lie b...

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)=r[4,) -u 82 – 64 P(X <82)= P| = P(Z < 2) :· By using Excel fn. = P(Z <2) =NORM.S.DIST(2,TRUE) = 0.9772 Thus, approximately 98 percent of the widget weights lie below 82 ounce.

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