A weekend TV game show called rolling a dice is running each week. For each roll, if the dice shows an odd number the participate earns 5 dollars and otherwise, he gets nothing. Each participate can roll the dice 20 times. Let X denote the number times the dice shows an odd number.

a)(2 mark) Calculate the average earning of a participate.

b)(4 marks) Calculate the probability that 2 (show your final answer correct to four decimal places).

c)(5 marks) 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 need to apply a continuity correction. That is

( ) ( + 0.5).

Calculating the probability that 6 by using Normal approximation with continuity correction.