Question $4$:

a$)$ A component is expected to encounter a maximum stress of $40,000$ psi. Past

data on similar components show that the standard deviation of strength is

about $10$ percent of the average strength. What specification should be set on

average strength to achieve a safety margin of $3\mathrm{.}0?4\mathrm{.}0?5\mathrm{.}0?($Assume that

strength is distributed normally.$)$

b$)$ Measurements were made on the bore dimension of an impeller. A sample of $20$

from a pilot run production showed a mean value of $9\mathrm{.}8576$ inches and a

standard deviation of $0\mathrm{.}00015$ inch. All the units functioned properly, and so it

was decided to use the data to set specification limits for regular production.

i$)$ Suppose it was assumed that the sample estimates were exactly equal to

the population mean and standard deviation. What specification limits

should be set to include $99$ percent of production?

ii$)$ There is uncertainty that the sample and population values are equal.

Based on the sample of $20,$ what limits should be set to be $95$ percent

sure of including $99$ percent of production?