Notice that the total probability is distributed in 8 minutes. Furthermore, the total probability has to be equal to 1, then:
[tex]\begin{gathered} h\cdot8=1 \\ \Rightarrow h=\frac{1}{8}=0.125 \end{gathered}[/tex]
Where h is the height of the distribution. The first answer is 0.125.
b) Notice that 16-13=3 min. Therefore, the probability we are looking for is:
[tex]P(13
The second answer is 0.375c) Notice that the probability for the bus to arrive before 15 minutes is:
[tex]P(X\le15)=\frac{15-9}{8}=\frac{6}{8}=0.75[/tex]
Thus, the probability that will we wait more than 15 minutes is:
[tex]P(X>15)=1-0.75=0.25[/tex]
The third answer is 0.25
d) The probability that one will wait at most 15 minutes was found in the previous step:
[tex]P(X\le15)=\frac{15-9}{8}=\frac{6}{8}=0.75[/tex]
The fourth answer is 0.75
