Question

in the 2016 rio olympics, ben proud swam the 50m freestyle in 21.54 seconds. assume that the distribution of swim times is normal with a mean swim time at the 2016 rio olympics of 21.765 seconds and a standard deviation of .252 seconds. about what proportion of swimmers swam faster than ben proud at the 2016 rio olympics

Answer 1

Explanation:

To answer this we calculate the z-score corresponding to x = 21.54 sec when the mean is 21.765 sec and the standard deviation is 0.252 sec:

21.54 sec - 21.765 sec

z = ------------------------------------- = = -0.893

0.252 sec

We interpret this result as follows: the desired proportion is the area under the standard normal curve between z = -0.893 and z = infinity, or between x = 21.54 and x = 10000

Using a calculator with built-in statistical functions (I'm using a TI-83 Plus), this area is

normcdf(21.54,10000,21.765,0.252) = 0.814