Four employees who work as drive-through attendants at a local fast-food restaurant are being evaluated.As part of a quality improvement initiative and employee evaluation,these workers were observed over three days.One of the statistics collected was the proportion of time the employee forgot to include a napkin in the bag.Related information is given in the table. $\begin{array}{lcc}
&\text { o of Dinners }&\text { o of Dinners Packed }\
\text { Worker } & \text { Packed } & \text { with No Napkin } \
\text { Joe } & 25 \% & 6 \% \
\text { Jan } & 20 \% & 2 \% \
\text { Cheryl } & 20 \% & 10 \% \
\text { Clay } & 35 \% & 4 \%
\end{array}$
You just purchased a dinner and found that there is no napkin in your bag.What is the probability that Cheryl prepared your order?
A)0.378
B)0.091
C)0.083
D)0.500
E)0.020

Question

Quizplus · Accepted Answer

The probability that Cheryl prepared the order given that there is no napkin is calculated using Bayes' theorem. Cheryl's probability of packing a dinner with no napkin is 0.20 * 0.10 = 0.02. The total probability of a dinner with no napkin is the sum of probabilities for all workers: (0.25 * 0.06) + (0.20 * 0.02) + (0.20 * 0.10) + (0.35 * 0.04) = 0.053. Thus, the probability is 0.02 / 0.053 = 0.378.

Four Employees Who Work as Drive-Through Attendants at a Local