Question $8,$ Problem $13$

HW Score: $74\mathrm{.}07\%,20$ of $27$

Part $1$ of $2$

points

Points: $0$ of $4$

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The IRS is concemed with improving the accuracy of tax information given by its representatives over the telephone. Previous studies involved asking a set of $25$ questions of a large number of IRS telephone representatives to determine the proportion of correct responses. Historically, the average proportion of correct responses has been $72$ percent. Recently, IRS representatives have been receiving more training. On April $26,$ the set of $25$ tax questions were again asked of $20$ randomly selected IRS telephone representatives. The proportions of correct answers were:

$22,21,19,16,15,16,21,21,17,21,24,16,23,15,21,19,23,17,21,$ and $10.$

a$.$ What are the upper and lower control limits for the appropriate p$-$chart for the IRS? Use $z=3.$

The $UC{L}_p$ equals and the $LC{L}_p$ equals $.($Enter your responses rounded to four decimal places. If your answer for $LC{L}_p$ is negative, enter this value as $0.)$