Question

In a e-sports racing tournament, the time playerispent (Ti, in seconds) oncompleting a certain track depends on two variables: the skill of playeri(Si), on a scale of0 to 10; and the quality of keyboard (Q), on a scale of 0 to 100. The relation among thevariables is given byTi= 300−5Si−2QFurther, suppose that the keyboards provided by the tournament are homogeneous and ofqualityQ= 100, and that the skills of all players in this tournament are approximatelynormally distributedwith mean 9, and standard deviation 0.32. In the following, we callTi, the record of playeri.

(a) Determine the distribution of the records in the tournament and specify its parameters.

(b) If a player in the tournament is randomly selected, what is the probability that shefinished the track within 55 seconds?

(c) Find the 10thpercentile of the records. (i.e., the record which only 10% of all the playersin the tournament can defeat.)

(d) Suppose that in order to advance to the final stage, a player needs to beat the record of52 seconds. What fraction of the players are able to advance to the final stage?

Answer 1