Question

Let X model the racing times for local high school track athletes in the 400-meter dash. Assume that X is normally distributed with a mean of 60 seconds and a standard deviation of 4.7 seconds. To go to the State Competition, a runner must have a 400-meter race time in the bottom 8% of times. If an athlete wants to go to the State Competition, what time must she/he beat? Please show how you get the z-score.

Answer 1

Given X is normally distributed with mean = 60 sec and standard deviation = 4.7 sec

We have to find bottom 8% of racing times X

X = + * Z​​​​​​0.08

where Z​​​​​0.08  is Z score corresponding to area to left of Z is 0.08

Using standard normal table ( Z table)

Z​​​​​​0.08 = -1.41

X = 60 + 4.7*(-1.41)

X = 53.37 seconds