NASCAR driver Matt Kenseth won the 2012 Daytona 500. His win was no surprise because for the 2011 season he finished fourth in the point standings with 2330 points. In 2011, he earned $6.184 million dollars by winning three Poles (fastest driver in qualifying), winning three races, finishing in the top five 12 times, and finishing in the top ten 20 times. NASCAR’s point system in 2011 allocated 43 points to the driver who finished first, 42 points to the driver who finished second, on down to 1 point for the driver who finished last. In addition, any driver who led a lap received 1 bonus point, the driver who led the most laps received an additional bonus point, and the race winner was awarded 3 bonus points. But, the maximum number of points a driver could earn in any race was 48. The accompanying spreadsheet contains the 2011 data for the top 35 NASCAR drivers. The variables include the drivers points for the season (POINTS), the number of poles won (POLES), the number of races won (WINS), the number of top 5 finishes (TOP5), and the number of top 10 finishes (TOP10), along with each drivers winnings (in millions of $).

1. Suppose that a driver has 22 top 10 finishes, 13 top 5 finishes, 3 wins, and no poles with a total of 2345 points for the season. How much should he expect to win?
 

Driver 1 Tony Stewart 2 Carl Edwards 3 Kevin Harvick 4 Matt Kenseth 5 Brad Keselowski 6 Jimmie Johnson 7 Dale Earnhardt Jr. 8 Jeff Gordon 9 Denny Hamlin 10 Ryan Newman 11 Kurt Busch 12 Kyle Busch 13 Clint Bowyer 14 Kasey Kahne 15 A.J. Allmendinger 16 Greg Biffle 17 Paul Menard 18 Martin Truex Jr. 19 Marcos Ambrose 20 Jeff Burton 21 Juan Montoya 22 Mark Martin 23 David Ragan 24 Joey Logano 25 Brian Vickers 26 Regan Smith 27 Jamie McMurray 28 David Reutimann 29 Bobby Labonte 30 David Gilliland 31 Casey Mears 32 Dave Blaney 33 Andy Lally 34 Robby Gordon 35 J.J. Yeley Points Poles 2403 2403 2345 2330 2319 2304 2290 2287 2284 2284 2262 2246 1047 1041 1013 997 947 937 936 935 932 930 906 902 846 820 795 757 670 572 541 508 398 268 192 1 3 0 3 1 0 1 1 0 3 3 1 0 2 0 3 0 1 0 0 2 2 2 2 0 0 1 1 0 0 0 0 0 0 0 Wins 5 1 4 3 3 2 0 3 1 1 2 4 1 1 0 0 1 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 Top5 9 99066 19 12 10 14 4 13 in 5 9 8 14 4 8 1 3 4 3 522 2 2 4 4 3 2 2 1 1 1 0 1 0 0 0 Top10 Winnings ($) 6.53 8.49 19 26 19 20 14 21 12 18 14 17 16 18 16 15 10 10 0 00 8 12 12 in 5 8 10 8 00 10 6 7 5 4 3 2 2 0 1 0 0 0 6.2 6.18 5.09 6.3 4.16 5.91 on 5.4 5.3 5.94 6.16 5.63 4.78 4.83 4.32 3.85 3.96 4.75 3.81 5.02 3.83 4.2 3.86 4.3 4.58 4.79 4.37 4.51 3.88 2.84 3.23 2.89 2.27 2.56