The manager of a bank recorded the amount of time each customer spent waiting in line during peak business hours one Monday. The frequency table below summarizes the results. $\begin{array}{|l|l|}
\hline \begin{array}{l}
\text { Waiting Time } \
\text { (minutes) }
\end{array} & \begin{array}{l}
\text { Number of } \
\text { Customers }
\end{array} \
\hline 0-3 & 9 \
\hline 4-7 & 10 \
\hline 8-11 & 12 \
\hline 12-15 & 4 \
\hline 16-19 & 4 \
\hline 20-23 & 2 \
\hline 24-27 & 2 \
\hline
\end{array}$

If we randomly select one of the customers represented in the table, what is the probability that the waiting time is at least 12 minutes or between 8 and 15 minutes?
A) $0.558$
B) $0.651$
C) $0.093$
D) $0.727$

Question

The manager of a bank recorded the amount of time each customer spent waiting in line during peak business hours one Monday. The frequency table below summarizes the results. $\begin{array}{|l|l|}
\hline \begin{array}{l}
\text { Waiting Time } \
\text { (minutes) }
\end{array} & \begin{array}{l}
\text { Number of } \
\text { Customers }
\end{array} \
\hline 0-3 & 9 \
\hline 4-7 & 10 \
\hline 8-11 & 12 \
\hline 12-15 & 4 \
\hline 16-19 & 4 \
\hline 20-23 & 2 \
\hline 24-27 & 2 \
\hline
\end{array}$

If we randomly select one of the customers represented in the table, what is the probability that the waiting time is at least 12 minutes or between 8 and 15 minutes?
A) $0.558$
B) $0.651$
C) $0.093$
D) $0.727$

Quizplus · Accepted Answer

The probability that the waiting time is at least 12 minutes is the sum of the probabilities that the waiting time is between 12 and 15 minutes and the probability that the waiting time is between 16 and 19 minutes. The probability that the waiting time is between 12 and 15 minutes is 4/33, and the probability that the waiting time is between 16 and 19 minutes is 4/33. Therefore, the probability that the waiting time is at least 12 minutes is 4/33 + 4/33 = 8/33 = 0.242. The probability that the waiting time is between 8 and 15 minutes is the sum of the probabilities that the waiting time is between 8 and 11 minutes and the probability that the waiting time is between 12 and 15 minutes. The probability that the waiting time is between 8 and 11 minutes is 12/33, and the probability that the waiting time is between 12 and 15 minutes is 4/33. Therefore, the probability that the waiting time is between 8 and 15 minutes is 12/33 + 4/33 = 16/33 = 0.485. The probability that the waiting time is at least 12 minutes or between 8 and 15 minutes is the sum of the probabilities that the waiting time is at least 12 minutes and the probability that the waiting time is between 8 and 15 minutes. Therefore, the probability that the waiting time is at least 12 minutes or between 8 and 15 minutes is 0.242 + 0.485 = 0.727.

The Manager of a Bank Recorded the Amount of Time