Z-scores

At the 2016 Olympic games Usain Bolt won the gold medal. In order to get to the finals he first had to qualify in the preliminary heats where he ran the 100m in 10.07 seconds. If the preliminary heats had

 $\overline{x}=10.3293$  and  $s_x=0.2709$  what was his standardized score for the preliminary heats?

• -0.9572

• -0.9571

• 0.9572

• 0.9571

In the same event, Justin Gatlin ran the 100m with a z-score for heat of -1.1787. How fast did he run (round to the nearest hundredth of a second)? 

(Remember that $\overline{x}=10.3293$  seconds and  $s_x=0.2709$  seconds.)

• 10.00 seconds

• 10.01 seconds

• 10.64 seconds

• 10.65 seconds

In 2016 Brianna Rollins ran her heat for the 100m hurdles in 12.54 seconds. If $\overline{x}=13.0857$  seconds and  $s_x=0.4671$  seconds, what was her standardized score?  Remember to round to four decimal places.

Also in the 100m hurdles in 2016, Kristi Castlin had a z-score of -0.8686 for her time in the preliminary heats. How fast did she run (to the nearest hundredth of a second) if $\overline{x}=13.0857$  seconds and  $s_x=0.4671$  seconds?

In the final Kristi Castlin ran the 100m hurdles in 12.61 seconds. What is her standardized score for the final using $\overline{x}=13.0857$  seconds and $s_x=0.4671$  seconds?  Remember to round to four decimal places.

Using the standardized scores calculated in the previous two problems for Kristi Castlin, did she do better in the "preliminary heat" or the "final"?

The second place finisher in the 2016 Women's 100m Hurdles was Nia Ali. Her standardized score for the preliminary heats was -0.6973. How fast did she run if $\overline{x}=13.0857$  seconds and $s_x=0.4671$  seconds?  (Round to the hundredth of a secocnd)

The runner in the 100m hurdles from Belize had a standardized score of 5.7896. Would you expect this to be a good time? Why or why not?

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What was the actual time for the runner from Belize (rounding to the hundredths of a second)? Remember that her standardized score is 5.7896, $\overline{x}=13.0857$ and  $s_x=0.4671$  

At the 2012 London Olympics, Michael Phelps won the 100m butterfly with a time of 51.21 seconds. What was his z-score if $\overline{x}=53.2177$  seconds and  $s_x=2.2867$  seconds?  Remember to round to four decimal places.