Question

Running a mile A study of $12,000$able-bodied male students at the University of Illinois found that their times for the mile run were approximately Normal with mean $7.11$ minutes and standard deviation $0.74$ minute. 7 Choose a student at random from this group and call his time for the mile Y. Find $P(Y<6)$. Interpret this value.

Short answer

The value of$P(Y<6)=6.68\%$

Step-by-step solution

Step 1. Given information.  

We have mean $7.11$minutes and standard deviation $0.74$minute.

Step 2. To find the value of  z. 

$$\begin{gathered} z=\frac{x-\mu }{\sigma } \\ z=\frac{6-7.11}{0.74} \\ z\approx -1.50 \end{gathered}$$

Step 3. To find the probability. 

$$\begin{gathered} P(Y<6)=P(Z<-1.50) \\ =0.0668 \\ =6.68\% \end{gathered}$$