Leah\'s Toys produces molded plastic baby rattles. These rattles must be complet

Question

Leah's Toys produces molded plastic baby rattles. These rattles must be completely smooth. That is, there can be no rough edges where the molded halves fit together. Rattles are judged to be either acceptable or defective with regard to this requirement. Leah's has determined that the current process has an underlying p value of 0.02, meaning that, on average, 2 out of 100 rattles is currently judged to be defective. Calculate the standard deviation for the process and the resulting control limits for samples of 900 rattles each. The standard deviation for the process is nothing. (Enter your response rounded to three decimal places.) The upper control limit is nothing. (Enter your response rounded to three decimal places.) The lower control limit is nothing. (Enter your response rounded to three decimal places.)

Explanation / Answer

P-bar = 0.02

Sample size = n = 900

Sp = sqrt of [P-bar (1-P-bar) /n]

= sqrt of [0.02(1-0.02) / 900]

= sqrt of (0.0196/900)

= 0.005

So the standard deviation of the process is 0.005

Upper control limit = P-bar + (3 x Sp)

= 0.02 + (3 x 0.005)

= 0.02 + 0.015

= 0.035

Lower control limit = P-bar - (3 x Sp)

= 0.02 - (3 x 0.005)

= 0.02 - 0.015

= 0.005

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