5. At 11 pm one evening, the Queen discovers that her carrying case of bespoke gloves has gone missing after her recent return from a trip overseas. She is due to

leave on a 30-day trip to Korea at 5 pm the next night. Her dresser Angela contacts her glove maker STAT 151 Genevieve, who says that she can order an emergency shipment of white sueded cotton from the United States to be flown overnight, and that her best emergency seamstresses, Catherine, Beatrice, and Eugenie, can sew new gloves tomorrow and that they will make a delivery of the gloves they make to the Queen at 4 pm tomorrow. If the shipment arrives on the 8 am train (best scenario), Catherine, the head seamstress, can make 24 pairs, Beatrice, the next most experienced seamstress, can make 20 pairs, and Eugenie, the next most experienced seamstress, can make 16 pairs before 4 pm. If the shipment arrives on the 10 am train (medium scenario), Catherine can make 18 pairs, Beatrice can make 15 pairs, and Eugenie can make 12 pairs before 4 pm. If the shipment arrives on the noon train (worse scenario) Catherine, the head seamstress, can make 12 pairs, Beatrice can make 10 pairs, and Eugenie can make 8 pairs before 4 pm. There is a 40% chance the shipment of white sueded cotton will arrive by 8 am, a 30% chance the shipment will not arrive until 10 am, and a 30% chance the shipment will not arrive until noon. Catherine 24 18 12 Beatrice 20 15 10 Eugenie 16 12 8 3 Best Case Medium Case Worse Case After a lifetime of service, Her Majesty Queen Elizabeth II sadly passed away at the age of 96 on September 8, 2022. This question is inspired by the article cited below. https://www.rd.com/article/queen-elizabeth-gloves/ a) Determine the expected number of gloves that can be made by each of the 3 seamstresses tomorrow. (6 marks) b) Will the Queen have enough gloves for 30 days, if she needs a new pair every day? (2 marks)