a weekend TV game show called lucky six is running each week. each participate have an Opportunity to roll a regular dice 5 times. for each roll, if the dice shows six, the participants earns 60 dollars and otherwise he gets nothing. let X denote the number of times the dice shows six. 1. calculate the average earning of a participate. 2. calculate the probability that the dice shows more then on six . 3. under appropriate condition, a Binomial random Variable X can be approximated by a normal random variable Y with the same mean and standard deviation. in doing so we neeed to apply a continuity correction. that is P(X^a)=(Y^a+0.5)

calculate the probability that X ^ 0 BY using normal approximation with continuity correction.