QUESTION $3$:

A work sampling study is to be performed on an insurance office staff consisting of $15$ persons to see

how much time they spend processing claims. The duration of the study is $20$ days, eight hours per day.

Processing claims is only one of the activities done by the staff members. The office manager estimates

that the proportion of time processing claims $=0\mathrm{.}20.($a$)$ At the $95$ percent confidence level, how many

observations are required if the upper and lower confidence limits are $0\mathrm{.}16$ and $0\mathrm{.}24?($b$)$ Regardless of

your answer to $($a$),$ a total of $1200$ observations were taken, and staff members were processing claims

in $300$ of those observations. Construct a $98$ percent confidence interval for the true proportion of time

processing claims. $($c$)$ Records for the period of the study indicate that $335$ claims were processed.

Estimate the average time per claim processed? $($d$)$ Determine a standard for processing claims, but

express the standard in terms of the number of claims processed per day $(8$ hours$)$ per person. Assume a

$100\%$ performance rating and that no allowance factor is to be included in the standard.