![]() Z-scores are used to calculate desired confidence intervals and the z-score used depends on the level of confidence required.Ĭonfidence intervals for a mean are written in the form: This process allows for a comparison to be made between the two races despite different mean times and standard deviations. In this example, a lower time would be preferable when completing a race and so, the lower z-score would be best. The z-score of 0.854 corresponds to a time which is greater than the mean time and is located on the right of the mean. We can see that the z score of -2 corresponds to a time which is less than the mean time and is located on the left of the mean. We can add 0.854 lots of the standard deviation to obtain the raw score: We can see that the mean is 125 and the standard deviation is 8.2. In the 500m race, the time is 0.854 standard deviations above the mean. Subtracting two lots of the standard deviation from the mean, we obtain the raw score: We can see that the mean is 31 and the standard deviation is 1.5. This means that the time in the 200m race is two standard deviations less than the mean time.
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