Find the specified probability.
-A statistics professor has office hours from 9:00 am to 10:00 am each day. The number of students waiting to see the professor is a random variable, X, with the distribution shown in the table. $\begin{array}{c|c|c|c|c|c|c}
\mathrm{x} & 0 & 1 & 2 & 3 & 4 & 5 \
\hline \mathrm{P}(\mathrm{X}=\mathrm{x}) & 0.05 & 0.10 & 0.40 & 0.25 & 0.15 & 0.05
\end{array}$
The professor gives each student 10 minutes. Determine the probability that a student arriving just after 9:00 am will have to wait no longer than 20 minutes to see the professor.
A)$0.40$
B) $0.55$
C) $0.80$
D) $0.15$

Question

Find the specified probability.
-A statistics professor has office hours from 9:00 am to 10:00 am each day. The number of students waiting to see the professor is a random variable, X, with the distribution shown in the table. $\begin{array}{c|c|c|c|c|c|c}
\mathrm{x} & 0 & 1 & 2 & 3 & 4 & 5 \
\hline \mathrm{P}(\mathrm{X}=\mathrm{x}) & 0.05 & 0.10 & 0.40 & 0.25 & 0.15 & 0.05
\end{array}$
The professor gives each student 10 minutes. Determine the probability that a student arriving just after 9:00 am will have to wait no longer than 20 minutes to see the professor.  
A)$0.40$
B) $0.55$
C) $0.80$
D) $0.15$

Quizplus · Accepted Answer

A student arriving just after 9:00 am will have to wait no longer than 20 minutes if there are 0, 1, or 2 students ahead of them, since each student takes 10 minutes. The probabilities for 0, 1, and 2 students are 0.05, 0.10, and 0.40, respectively. Adding these probabilities gives 0.05 + 0.10 + 0.40 = 0.55.

Find the Specified Probability The Professor Gives Each Student 10 Minutes