The United Association (UA) is going to reserve a number of tickets for a concert held in Sydney Opera House in February 2019. Based on a survey on its members, the UA believes the number of tickets requested is normally distributed with a mean of 500 and a standard deviation of 80 . The UA can reserve tickets now (six months prior to the concert) for $100 each; however, for any tickets quested beyond the reserved now, the cost will be at the regular price of $150. The UA guarantees the ticket price of $100 to its members. If its members request fewer than the number of tickets it reserves, the UA must pay the concert organiser for the difference with a discount, at $70 for each remaining ticket reserved one week before the concert.