Question

Two sprinters, Nick and Ryan, want to find out who has the faster time when compared to each of their teams. Nick has a time of 10.8 seconds, and his team has a mean time of 11.4 seconds and a standard deviation of 0.4 seconds. Ryan has a time of 11.2 seconds, and his team has a mean of 11.5 seconds and a standard deviation of 0.1 seconds. Who has the faster time when compared to each of their teams?a) Nick b) Ryan c) The times are equal when compared to each of their teams.d) There is not enough information

Answer 1

Given data:

The time taken by Nick is 10.8 seconds.

The mean time taken by Nick is 11.4 seconds.

The given standard deviation of Nick is 0.4 seconds.

The time taken by Ryan is 11.2 seconds.

The mean time taken by Ryan is 11.5 seconds.

The given standard deviation of Ryan is 0.1 seconds.

The z-score of Nick is,

`\begin{gathered} z=(10.8-11.4)/(0.4) \\ =\text{ -1.5} \end{gathered}`

The z-score of Ryan is,

`\begin{gathered} z=(11.2-11.5)/(0.1) \\ =\text{ -3} \end{gathered}`

Thus, Ryan z-score is lower, so Ryan has the faster time when compared to each of their teams, option (b) is correct.