Question

The top three finishers in the Women’s 200m Dash at each Olympics dating back to 1988 have a mean of 22.04 seconds and a standard deviation of 0.24 seconds. In 2000, Pauline Davis won gold with a time of 22.27 seconds. What was her z-score? Remember to round z-scores to 2 decimal places.

Answer 1

`\mu = 22.04` represent the mean in seconds for the 200 m Dash in 1988

`\sigma = 0.24` represent the deviation in seconds for the 200 m Dash in 1988

We assume that the parameters are the same for 2000. And we know that Pauline Davis won gold with a time of 22.27 seconds, we want to find the z score so we can use the following formula:

`z=(X -\mu)/(\sigma)`

And replacing we got:

`z= (22.27- 22.04)/(0.24)= 0.96`

Explanation:

For this case we have the follwing parameters given:

`\mu = 22.04` represent the mean in seconds for the 200 m Dash in 1988

`\sigma = 0.24` represent the deviation in seconds for the 200 m Dash in 1988

We assume that the parameters are the same for 2000. And we know that Pauline Davis won gold with a time of 22.27 seconds, we want to find the z score so we can use the following formula:

`z=(X -\mu)/(\sigma)`

And replacing we got:

`z= (22.27- 22.04)/(0.24)= 0.96`