Question 2 Sandy is running a small business working on hand-made accessories. She has a customer, Jenny, who orders different items every day. After receiving Jenny’s order, Sandy packs a parcel for Jenny and makes delivery through the delivery service in her building. The delivery fee of a parcel is calculated based on the weight of the content, which is $0.033 per gram. According to Sandy’s record, the delivery fee of Jenny’s daily parcel follows a normal distribution with mean $66 and standard deviation $12.4. A parcel is classified as a deluxe parcel if the delivery fee is more than $100. It takes 2 working days to deliver a deluxe parcel and 4 working days to deliver the other parcel. (a) What is the probability that a Jenny’s parcel would be delivered in 2 working days? (b) There are 10% of the delivery fee of Jenny’s parcel are less than $K. What is the value of K? Instead of delivering Jenny’s parcel every day, Sandy is planning to combine two days’ order and pack Jenny a parcel for every two days. (c) What are the expectation and standard deviation of the delivery fee of the parcels, after combining two days’ order as one parcel? (d) What is the probability that the parcel would be delivered to Jenny in 2 working days, after combining two days’ order as one parcel? (e) If you were Jenny, would you like to have the orders combined? Explain your answer briefly by considering when you were likely to receive your first day order for the two cases (i) one parcel each day and (ii) one parcel every two days
Question 2 Sandy is running a small business working on hand-made accessories. She has a customer, Jenny, who orders different items every day. After receiving Jenny’s order, Sandy packs a parcel for Jenny and makes delivery through the delivery service in her building. The delivery fee of a parcel is calculated based on the weight of the content, which is $0.033 per gram. According to Sandy’s record, the delivery fee of Jenny’s daily parcel follows a
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