Question

a runner for team 1 can run a race in 58.2 seconds. team 1 has running times with a mean of 64.2 seconds and a standard deviation of 1.2 seconds. a runner for team 2 can run a race in 56.7 seconds. team 2 has running times with a mean of 62.1 seconds and a standard deviation of 4.4 seconds.
a) which runner is faster?
(this is not a trick question...no statistics involved here)
o runner for team 2
o runner for team 1
b) what is the z - score associated with the running time of runner for team 1?
round final answer to two decimal places.
c) what is the z - score associated with the running time of runner for team 2?
round final answer to two decimal places.
d) which runner is faster relative to their corresponding populations?
(now you have to use statistics)
o runner for team 2
o runner for team 1

Explanation:

Step1: Recall z - score formula

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x$ is the individual value, $\mu$ is the mean and $\sigma$ is the standard deviation.

Step2: Calculate z - score for team 1 runner

For team 1, $x = 58.2$, $\mu=64.2$, $\sigma = 1.2$. Then $z_1=\frac{58.2 - 64.2}{1.2}=\frac{- 6}{1.2}=-5.00$.

Step3: Calculate z - score for team 2 runner

For team 2, $x = 56.7$, $\mu = 62.1$, $\sigma=4.4$. Then $z_2=\frac{56.7-62.1}{4.4}=\frac{-5.4}{4.4}\approx - 1.23$.

Step4: Compare z - scores

A more negative z - score indicates a faster time relative to the team's mean. Since $-5.00<-1.23$, the team 1 runner is faster relative to their team.

Answer:

b) -5.00
c) -1.23
d) runner for team 1