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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

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altavistard

Answer:

Step-by-step 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

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