Question

I recently competed in a 5K race that had a mean finish time of µ = 24.3 minutes and standard deviation σ = 4.7 minutes. The finish times were normally distributed. Would either of these finish times be considered unusual? Explain.

a) 17.9 minutes

b) 34.6 minutes

If my finish time was 22.9 minutes,

a) Calculate the z-score for my time.

Answer 1

Any z-score greater than 3 or less than -3 is considered to be an outlier. This rule of thumb is based on the empirical rule. From this rule we see that almost all of the data (99.7%) should be within three standard deviations from the mean.

a) Thus, if we get u - 3* = 24.3 - 3*4.7 = 10.2

17.9 min is not unusal (as it is above 10.2)

b) u + 3* = 24.3 - 3*4.7 = 38.4

Thus, 34.6 is not unusual (as it is below 38.4)

c)

x = 22.9

z= (x - u)/σ

Thus, z = (22.9 - 24.3)/4.7

z = -0.2978

rounding off to -0.30