Question

44. Manufacturing Ball bearings are manufactured with a mean diameter of 5 millimeters (mm). Because of variability in the manufacturing process, the diameters of the ball bearings are approximately normally distributed, with a standard deviation of 0.02 mm. (a) What proportion of ball bearings has a diameter more than 5.03 mm

Answer 1

Answer:

0.0668 = 6.68% of ball bearings has a diameter more than 5.03 mm

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$, the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Manufacturing Ball bearings are manufactured with a mean diameter of 5 millimeters (mm).

This means that $\mu = 5$

With a standard deviation of 0.02 mm.

This means that $\sigma = 0.02$

(a) What proportion of ball bearings has a diameter more than 5.03 mm

This is 1 subtracted by the pvalue of Z when X = 5.03. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{5.03 - 5}{0.02}$

$Z = 1.5$

$Z = 1.5$ has a pvalue of 0.9332

1 - 0.9332 = 0.0668

0.0668 = 6.68% of ball bearings has a diameter more than 5.03 mm