Question

In order to meet the specifications of a client, a manufacturer of widgets needs to make their widgets 1200 mm long. A quality assurance expert randomly selects 159 widgets and calculates the mean length to be 1202 mm with a standard deviation of 1.24 mm.

1. Determine the percent of widgets that fall between 1200 mm and 1205 mm.
2. If a widget is randomly selected, determine the probability that its length is greater than 1197 mm.
3. If a widget is randomly selected, determine the probability that its length is greater than 1207 mm.
4. If a widget is randomly selected, determine the probability that its length is less than 1203.5 mm.
5. If a widget is randomly selected, determine the probability that its length is between 1196 mm and 1201 mm.
6. If the client is will accept a 5 mm tolerance, do you think that the manufacturer should re-calibrate its equipment?

Answer 1

f. Since 99.73% values lie within 3 sigma limits ( 1202-3*1.24,1202+3*1.24)=(1198.28,1205,72), the manufacturer need not to calibrate to accomodate 5 mm tolerance. In fact 99.73% values satisfy 3.72mm tolerance and hence are mostly within 5mm tolerance.