Ball-Bearings,Inc. produces ball bearings automatically on a Kronar BBX machine. For one of the ball bearings,the mean diameter is set at 20.00 mm (millimeters). The standard deviation of the production over a long period of time was computed to be 0.150 mm. What percent of the ball bearings will have diameters of 20.27 mm or more?
A)41.00%
B)12.62%
C)3.59%
D)85.00%

Question

Quizplus · Accepted Answer

To find the percentage of ball bearings with diameters of 20.27 mm or more, we use the Z-score formula: Z = (X - μ) / σ, where X is the value in question (20.27 mm), μ is the mean (20.00 mm), and σ is the standard deviation (0.150 mm). Plugging in the values, we get Z = (20.27 - 20.00) / 0.150 = 1.8. Looking up 1.8 on a standard normal distribution table or using a calculator, we find that the area to the left of Z = 1.8 is approximately 0.9641, which means 96.41% of the values lie below 20.27 mm. Therefore, 100% - 96.41% = 3.59% of the ball bearings will have diameters of 20.27 mm or more.