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 at least 30 minutes to see the professor.
A) 0.25
B)0.85
C)0.15
D)0.45

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 at least 30 minutes to see the professor.
A) 0.25
B)0.85
C)0.15
D)0.45

Quizplus · Accepted Answer

For a student to wait at least 30 minutes, there must be at least 3 students ahead of them because each student takes 10 minutes. The probability for 3 or more students is P(X=3) + P(X=4) + P(X=5) = 0.25 + 0.15 + 0.05 = 0.45.

Find the Specified Probability The Professor Gives Each Student 10 Minutes