A manufacturer contracts to supply ball bearings with diameters between 24.5 mil

Question

A manufacturer contracts to supply ball bearings with diameters between 24.5 millimeters and 25.3 millimeters. Product analysis indicates that the ball bearings manufactured have diameters that are normally distributed with a mean of 25.10 millimeters and a standard deviation of 0.20 millimeters. Use the 68 -­ 95 -­ 99.7 rule to find the proportion of ball bearings that FAILY TO SATISFY the contract specificatications.

I got 15% or so (can't remember the exact number), but I was wondering if this was correct.

Explanation / Answer

68-95-99.7 rule is that 68% and 95% and 99.7% of the data lies between the 1,2,3 standard deviations.

Mean=25.1,standard dev=0.2

Hence withing 1 std dev=(25.1-0.2,25.1+0.2) =(24.9,25.3)----------------->68% of data

Hence between 1 and 2 standard dev=(24.9-0.2,25.3+0.2)=(24.7,25.5)------------->95-68 =27% data

Hence between 2 and 3 standard dev=(24.7-0.2,25.5+0.2)=(24.5,25.7)----------->99.7-95=4.7% data

But the supply we got was between 24.5 to 25.3 mm

Hence we have 68+27/2+ 4.7/2 % =83.85%

Hence the ball bearings failing to satisfy=100-83.85 =16.15%

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