The number of yards gained is rightskewed and therefore a no

The number of yards gained is right-skewed and therefore a normal model is NOT a good model for the data. However, the square root of the number of yards gained can be approximated very well by a N(21.5, 8.3) model. A particular wide receiver has a bonus clause in his contract that pays him a bonus of $1 million if his yards gained are in the top 10% of yards gained by wide receivers. How many yards does this receiver have to gain to get the bonus?

Solution

Top 10% means, a Z-score corresponding to the 90% confidence level (1-tail).

Z = 1.28

So, Y = 21.5 + 1.28 * 8.3 = 32.124

No. of yards = Y^2 = 1031.951376