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 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 Best Case 24 Medium Case Worse Case 18 12 Beatrice 20 15 10 Eugenie 16 12 8 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) c) Compute the standard deviation for Eugenie's gloves. (3 marks) 6. Linus Ullmark of the Boston Bruins had the best save percentage of a goalie in the 2022-2023 season. We take this to mean, loosely, that Ullmark has a 93.8% chance of making a save when a puck is shot at his goal. In a practice in the 2023-2024 season, a fellow Bruin makes 20 shots on Ullmark. a) What is the probability that Ullmark will make saves on more than 18 shots on goal? (4 marks) b) What is the probability that he will miss stopping (allow) at least 2 of the shots on goal? (4 marks) c) How many shots on goal do you expect Ullmark to stop? (2 marks) d) Obtain the standard deviation of the number of shots on goal that Ullmark will stop. (2 marks)