Chapter 6.1, Problem 27E

To determine

To find: probability $\text{P}\left(Y<6\right)$ and explain it

Answer to Problem 27E

  $\text{P}\left(Y<6\right)=0.0668$

Explanation of Solution

Given:

  $\begin{array}{l}\mu =7.11\\ \sigma =0.74\end{array}$

Formula used:

  $z=\frac{x-\mu }{\sigma }$

Calculation:

  $\begin{array}{l}z=\frac{x-\mu }{\sigma }\\ =\frac{6-7.11}{0.74}\\ z=-1.5\end{array}$

  $\begin{array}{c}\text{P}\left(X<6\right)=\text{P}\left(Z<-1.5\right)=0.0668\\ =6.68\%\end{array}$

  

Probability for less than 6 is 0.0668 which imply that 6.68 percent that the student would run a time of less than 6 minute.