In a game, a player needs to throw a ball as far as possible. They win the amount of…

MATHEMATICS · Multi-part · AP · AP Statistics · Probability Random Variables Distributions · Probability Random Variables Distributions

Problem

In a game, a player needs to throw a ball as far as possible. They win the amount of money (in Yen) equal to the length of the throw, in metres. Let XX be the continuous random variable modelling the length of a throw. It is assumed that no one can throw further than 10 m, and that the probability density function of XX is f(x)=0.328exex+e7 for 0≤x≤10f(x) = \frac{0.328e^x}{e^x + e^7} \text{ for } 0 \le x \le 10 (a) How much should be charged per game in order to make the game fair? (b) What percentage of players are expected to make a profit from this game?

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