Problem $7-13($Algo$)$

In an initial survey designed to estimate the percentage of time air$-$express cargo loaders are idle, an analyst found that loaders were

idle in $6$ of the $45$ observations.

a$.$ What is the estimated percentage of idle time? $($Round your answer to $2$ decimal places.$)$

b$.$ Based on the initial results, approximately how many observations would you require to estimate the actual percentage of idle time

to within $5$ percent with a confidence of $95$ percent? $($Round your $z$ value to $2$ decimal places. Do not round any other intermediate

calculations. Round UP your final answer to the next whole number.$)$