Question

A- 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 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 A-1. Use the normal model to determine the probability that a wide receiver gained 310 yards or less during the season. (Use 4 decimal places).

Question A-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 10% of yards gained by wide receivers. How many yards does this receiver have to gain to get the bonus? (Round to nearest yard). yards

B- The Apple, Inc. sales manager for the Chicago West Suburban region is disturbed about the large number of complaints her office is receiving about defective ipods. New Apple CEO Tim Cook is also very displeased and wants the situation remedied as soon as possible.

The sales manager examines this Excel file ipod Weekly Complaints, which shows the number of complaints concerning defective ipods received by her office for each of the immediately preceding 52 weeks.

Question B-1.What is the probability that between 78 and 113 complaints are received in one week? Use a N(108,20) model to approximate the distribution of weekly complaints.

Question B-2. Tim Cook decrees that the next time the number of complaints received in one week exceeds the value of the third quartile Q₃, he will register a strong complaint with the ipod assembly plant in China. What is the value of Q₃? (Note: as in question 2, use a N(108,20) model to approximate the distribution of weekly complaints). Use 1 decimal place in your answer.

Q₃.

Answer 1