Sampling From A Non-Normal Population (Central Limit Theorem)

An electronics shop is offering lucky draws to customers. An eligible customer can choose to enter the lucky draw to win either a cash prize or discount voucher prize. On average, for each customer, there is a one in every \(25\) chances of winning a cash prize and a one in every \(5\) chances of winning a discount voucher price. On each day, \(100\) customers tried for a cash prize and \(280\) customers tried for a discount voucher prize. Estimate the probability that for \(40\) randomly selected days, the average number of customers who won a cash prize differ from the average number of customers who won a discount voucher prize by \(50\) customers.