A machine that produces ball bearings has initially been set so that the true av

Question

A machine that produces ball bearings has initially been set so that the true average diameter of the bearings it produces is 0.500 in. with a standard deviation of 0.002 in. A bearing is acceptable if its diameter is within 0.004 in. of this target value. a What percentage of the bearings produced by the machine will not be acceptable? b Suppose that the setting has changed during the course of production, so that the bearings have normally distributed diameters with mean value 0.499 in. and a standard deviation of 0.002 in. What percentage of the bearing produced in this setting will not be acceptable?

Explanation / Answer

A) The acceptable range of within 0.004 in frm0.5 in is equal to 2 standard deviations from the mean. So, according to the emperical formula, 95.45% of bearing produced will be acceptable.

So, percentage of bearing that will not be acceptable = 100 - 95.45 and = 4.55%

B) Acceptable range = 0.496 to 0.504 inch

P(x < 0.496) = P(Z < (0.496 - mean)/standard deviation)

= P(Z < (0.496 - 0.499)/0.002)

= P(Z < -1.5)

= 0.0668

P(x>0.504) = 1 - P(Z < (0.504 - 0.499)/0.002)

= 1 - P(Z < 2.5)

= 1 - 0.9938

= 0.0062

So, the percentage of bearing produces in this setting, that will not be accepted = (0.0668 + 0.0062)x100 = 7.3%

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