Question

Two sprinters, Nick and Ryan, want to find out who has the faster time when compared to each of their teams. Nick has atime of 108 seconds, and his team has a mean time of 114 seconds and a standard deviation of 0.4 seconds. Dan has atime of 11.2 seconds, and his team has a mean of 115 seconds and a standard deviation of 0.1 seconds. Who has thefaster time when compared to each of their teams

Answer 1

For Nick, we have the following information:

`\begin{gathered} x=10.8,\mu=11.4,\sigma=0.4 \\ \Rightarrow z=(x-\mu)/(\sigma)=(10.8-11.4)/(0.4)=-1.5 \end{gathered}`

For Ryan, we have the following:

`\begin{gathered} x=11.2,\mu=11.5,\sigma=0.1 \\ \Rightarrow z=(11.2-11.5)/(0.1)=-3 \end{gathered}`

Notice that the z score for Ryan is greater than the z score for Nick, this means that the speed for Ryan is greater compared to his team. Therefore, the correct option is Ryan