Assume that the weights are roughly bell shaped If the weigh

Assume that the weights are roughly bell shaped. If the weights of quarters have a mean (w) = 5.67 grams and the standard deviation (sigma) = .06 grams:

If you have a vending machine which accepts weights between 5.64 and 5.70, what percentage of quarters will be rejected? (Z-table)

If another vending machine accepts all quarters, except those with weights in the 2.5% and the bottom 2.5%, what are the limits of the weights that are accepted; i.e. between what range of weights are acceptable? (Z-table)

Solution

As bell shaped we assume that it is normal with mu = 5.67 and sigma =0.06 gms

5.64<x<5.70

Convert x score into z score to find the percentage of rejections.

For 5.64, z = -0.03/0.06 = -0.5

For 5.70 z = +0.5

Rejection region = 1-P(-0.5<z<0.5)

= 1-0.3830

= 0.6170

IN percentage 61.70% will be rejected.

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Next machine rejection is when |z| value is > 2.81

i.e. x value lies between 5.67-2.81(0.06), 5.67+2.81(0.06)

=(5.36, 5.98) the weights can be acepted