Question

No downloads please!!! When Julian runs the 400 meter dash, his finishing times are normally distributed with a mean of 82 seconds and a standard deviation of 0.5 seconds. What percentage of races will his finishing time be faster than 82 seconds, to the nearest tenth?

Answer 1

Solution

For this case we have the following distribution:

$X\approx N(\mu=82,\sigma=0.5)$

and we want to find this probability:

$p(X>82)=1-p(X<82)$

We can use the z score formula and we got:

$z=\frac{X-\mu}{\sigma}=\frac{82-82}{0.5}=0$

Using the normal distribution table we got:

$P(Z>0)=1-0.5=0.5$

Then the final answer is 0.5