The manager of the Burger Doodle restaurant believes the time to fill orders at the drive-through window is too long. She suspects that the window cashier spends too much time making change, and she is considering using even pricing for most menu items to reduce the window time. She has decided to conduct a work sampling study to determine the proportion of time the cashier is making change. During a three-day period the manager checked the cashier 150 times and recorded 84 observations in which the cashier was making change.
a. How many more observations should be taken if the manager wants to be 99% confident that her estimate is within ±1% of the actual proportion of time the cashier is making change?
b. Based on the time required to take the first 150 observations, how many days will be required to conduct this study?
c. How could the manager reduce the number of days required to conduct in part (b)?