Question

multiple answer 10 points. the running times for the 100 are posted by the ohs track team is approximately normal with a mean time 13.4 seconds with a standard deviation of 1.6 sec. select the most appropriate answer(s) for a player who ran an 8.6. the time is about average relative to other runners. the players time is too far to the right. the players time is in the 3 sd to the left. the players time is an anomaly. the time is not even in the distribution.

Explanation:

Step1: Calculate z - score

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x = 8.6$, $\mu=13.4$, and $\sigma = 1.6$. So $z=\frac{8.6 - 13.4}{1.6}=\frac{-4.8}{1.6}=-3$.

Step2: Analyze z - score in normal distribution

In a normal distribution, about 99.7% of the data lies within 3 standard - deviations of the mean ($z$ values between - 3 and 3). A $z$ - score of - 3 means the value is 3 standard deviations to the left of the mean. Values that are more than 3 standard deviations from the mean are considered anomalies.

Answer:

The player's time is in the 3 SD to the left
The player's time is an anomaly