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 490 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 12% of yards gained by wide receivers. How many yards does this receiver have to gain to get the bonus? (Round to nearest yard).

Chad Johnson 1369 Marvin Harrison 1366 Reggie Wayne 1310 Roy Williams 1310 Donald Driver 1295 Lee Evans 1292 Anquan Boldin 1203 Torry Holt 1188 Terrell Owens 1180 Steve Smith 1166 Andre Johnson 1147 Laveranues Coles 1098 Isaac Bruce 1098 Mike Furrey 1086 Javon Walker 1084 T.J. Houshmandzadeh 1081 Joey Galloway 1057 Terry Glenn 1047 Marques Colston 1038 Plaxico Burress 988 Hines Ward 975 Jerricho Cotchery 961 Darrell Jackson 956 Larry Fitzgerald 946 Mark Clayton 939 Braylon Edwards 884 Muhsin Muhammad 863 Eddie Kennison 860 Santonio Holmes 824 Reggie Brown 816 Keyshawn Johnson 815 Santana Moss 790 Bernard Berrian 775 Reche Caldwell 760 Derrick Mason 750 Marty Booker 747 Devery Henderson 745 Bryant Johnson 740 Drew Bennett 737 Antonio Bryant 733 Ronald Curry 727 Deion Branch 725 Donte' Stallworth 725 Wes Welker 687 Arnaz Battle 686 Joe Horn 679 Chris Chambers 677 Eric Parker 659 Travis Taylor 651 Matt Jones 643 Greg Jennings 632 Nate Washington 624 Reggie Williams 616 D.J. Hackett 610 Chris Henry 605 Samie Parker 561 Eric Moulds 557 Randy Moss 553 Ernest Wilford 524 Patrick Crayton 516 Rod Smith 512 Roddy White 506 Cedrick Wilson 504 Joe Jurevicius 495 Kevin Curtis 479 Hank Baskett 464 Bobby Wade 461 Troy Williamson 455 Vincent Jackson 453 Keenan McCardell 437 Michael Jenkins 436 Ashley Lelie 430 Josh Reed 410 Peerless Price 402 Demetrius Williams 396 Terrance Copper 385 Troy Brown 384 Brandon Jones 384 Marcus Robinson 381 Brandon Lloyd 365 Amani Toomer 360 Ruvell Martin 358 Drew Carter 357 Michael Clayton 356 Antwaan Randle El 351 Greg Lewis 348 Justin McCareins 347 Doug Gabriel 344 Ike Hilliard 339 Roscoe Parrish 320 Brandon Marshall 309 Billy McMullen 307 Rashied Davis 303 Alvis Whitted 299 Bobby Engram 290 Mark Bradley 282 Tim Carter 253 Dennis Northcutt 228 Derek Hagan 221 Malcom Floyd 210 Troy Walters 209 Dante Hall 204 David Tyree 197 Nate Burleson 192 David Kircus 187 Corey Bradford 164 Kevin Walter 160 Bethel Johnson 156 Chad Jackson 152 James Thrash 151 Bryan Gilmore 150 Az-Zahir Hakim 147 John Madsen 146 Jabar Gaffney 142 Shaun McDonald 136 Carlyle Holiday 126 Roydell Williams 121 Kelley Washington 115 Tim Dwight 112 Jamal Jones 108 David Givens 104 Maurice Stovall 102 Mike Williams 99 Josh Cribbs 91 Koren Robinson 89 Brandon Stokley 85 Doug Gabriel 84 Aaron Moorehead 82 Tab Perry 81 Sam Hurd 75 Johnnie Morant 70 Jason Avant 68 Justin Gage 68 Paris Warren 63 Brad Smith 61 Keary Colbert 56