Question

Data from the National Football League (NFL) from a recent season reported the number of yards gained by each of the league's wide receivers. The data in this Excel file nfl_receiver_yds_webassign shows the yards gained by each wide receiver in the NFL who gained 50 or more yards during the season. 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.
Question 1. Use the normal model to determine the probability that a wide receiver gained 305 yards or less during the season. (Use 4 decimal places).

Question 2. 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 11% of yards gained by wide receivers. How many yards does this receiver have to gain to get the bonus? (Round to nearest yard). yards

Answer 1

Answer:

Question 1

The probability that a wide receiver gained 305 yards or less during the season is 0.3409

Question 2

number of yards = 32.124

Explanation:

The problem is basically saying that the data for the square roots of each of the players number of yards is normally distributed with a mean of 21.5 yards and a standard deviation of 8.3 yards. Once you know this, you can work with the square rooted values and the normal distribution curve. So for the first problem, you would use sqrt(325) = 18.02775, and then you could use a calculator to find the probability that a receiver had fewer yards than that based on the sd and mean, or you could find a z-score for 18.02775 and use a normal distribution table. You can use similar logic for the second question, but working backwards starting with the known percentage.

Question 1

The probability that a wide receiver gained 305 yards or less during the season is 0.3409

Question 2

Top 10% means you need a Z-score corresponding to the 90% confidence level (1-tail). I believe that value is Z = 1.28

So, look at 21.5 + 1.28 * 8.3 = Y.  Y^2 = number of yards

= 32.124