Problem $1-(10$ pts$)$

In an assembly line, the production manager must ensure that the correct quantities of components

are available for each unit. For a specific product, the manager needs to determine the appropriate

t$-$values to ensure component quantities meet certain confidence levels. Given the following

requirements:

$($a$)15$ bearings at $99\%$ confidence

$($b$)10$ gears at $90\%$ confidence

$($c$)8$ pistons at $95\%$ confidence

$($d$)25$ bolts at $99\mathrm{.}9\%$ confidence