The thickness in millimeters of the coating applied to disk

The thickness (in millimeters) of the coating applied to disk drives is a characteristic that determines the usefulness of the product. When no unusual circumstances are present, the thickness (x) has a normal distribution with a mean of 3 mm and a standard deviation of 0.06 mm. Suppose that the process will be monitored by selecting a random sample of 12 drives from each shift\'s production and determining x, the mean coating thickness for the sample. (Round all your intermediate calculations to four decimal places. Round the answers to four decimal places.)

(b) When no unusual circumstances are present, we expect x to be within 3?_x of 3 mm, the desired value. An x value farther from 3 than 3?_x is interpreted as an indication of a problem that needs attention. Compute 3

Solution

Mean =3 and std dev= 0.06

Sample size =12

For X to life within + or - 3 sigma is

prob = 0.9974 (From std normal distribution table)

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3+3sigma x = 3.06, 3-3sigma x = 2.94

Thus x lies between 2.94 and 3.06 is equivalent to

Z lying between -3.46<z<0 = 0.4997