In 2005, 1,475,623 students heading to college took the SAT….

In 2005, 1,475,623 students heading to college took the SAT. The distribution of scores in the math section of the SAT follows a normal distribution with mean µ= 510 and standard deviation σ= 125.  Calculate the z-score for an SAT score of 470. Interpret it using a complete sentence.

You decide to spend the weekend gambling with some friends. …

You decide to spend the weekend gambling with some friends.  You all bet on the Panthers game.  If your spread of the score is closest you make $150.  You and 19 of your friends each contribute $10.  What is the expected net value of the payoff?  Show your work