Question

X~(129.71,2.28) find the percent of her laps that are completed in less than 135 seconds

Answer 1

For this case we have the mean, which is 129.71 and the standard deviation 2.28. We need to first calculate the z value, which is given by the following expression:

$z=\frac{x-\operatorname{mean}}{\sigma}$$z=\frac{135-129.71}{2.28}=\frac{5.29}{2.28}=2.32017$

Now we need to look at the z-table to determine the percentage that is less than 135. From there we obtain the following:

$\text{percentage}=0.9898\cdot100\text{ \%=98.98 \%}$

A total of 98.98% of her runs will be less than 135 seconds.