Question

The run times of a marathon runner are approximately normally distributed. The z-score for his run this week is -2. Which one of the following statements is a correct interpretation of his z-score?

1) His run time is 2 standard deviations below the mean.
2) His run time is 2 standard deviations above the mean.
3) His run time is 2 standard deviations away from the mean.
4) His run time is 2 standard deviations closer to the mean.

Answer 1

His run time is 2 standard deviations below the mean.

The z-score of -2 means that the marathon runner's run time this week is 2 standard deviations below the mean of his run times.

Step-by-step explanation:

The z-score of -2 indicates that the marathon runner's time was 2 standard deviations below the mean of his run times. A negative z-score reflects a value below the mean, while a positive z-score indicates a value above the mean.

The correct interpretation of the runner's z-score would be that his run time this week is 2 standard deviations below the mean run time.

A z-score of -2 indicates that the student's run time is 2 standard deviations below the mean run time. In a normal distribution, about 95% of values fall within 2 standard deviations of the mean, so being 2 standard deviations below the mean is quite far from the average.

Therefore, option 1) His run time is 2 standard deviations below the mean is the correct interpretation of the z-score.

The z-score of -2 means that the marathon runner's run time this week is 2 standard deviations below the mean of his run times.