A petrol company issues a voucher with every 10 litres of petrol that a customer buys. Customers who send 50 vouchers to head office are entitled to a free gift but only one gift per household. After this promotion has been running for some time the company recieves several hundred bundles of vouchers in each day's post. It would take a long time and not cost effective for someone to count each bundle so they decide to weigh them instead. Working on the basis that the weight of a single voucher is a normal variable with mean 40mg and standard deviation 4mg they decide to calculate the weight which will be exceeded by 95% of the bundles and only count the numbers of vouchers in budles which weigh less than this calculated amount.
A man has 149 vouchers, divides these into 3 bundles without checking the number in each bundle carefully, and sends one claim for a gift in his own name and two claims in his friends names. Assess the likelihood that he will recieve all 3 gifts using relevant calculations. Give details of any assumptions you have made.