In an optical shop, the optician has conducted a survey with his customers with a question “how many pairs of sunglasses do you have?”. The result shows that 30% of the interviewees have 1 pair of sunglasses, 15% of the interviewees have 2 pairs of sunglasses and 15% of the interviewees have more than 2 pairs of sunglasses. The other interviewees do not have any sunglasses. The shop is organizing a private sale and there will be 20 participants. Peter is assigned to take care of those participants who says that they do not have any sunglasses. (a) What is the probability that a participant does not have any sunglasses? (b) Most likely, how many participants in the private sale do not have any sunglasses? Calculate the probability of its happening. (c) Peter is asking for an assistant for the private sales. His application should be approved if the probability that there will be more than 4 participants in the private sale have no sunglasses is higher than 0.8. Would his application be approved? Explain your answer with calculation.
In an optical shop, the optician has conducted a survey with his customers with a question “how many pairs
of sunglasses do you have?”. The result shows that 30% of the interviewees have 1 pair of sunglasses, 15%
of the interviewees have 2 pairs of sunglasses and 15% of the interviewees have more than 2 pairs of sunglasses.
The other interviewees do not have any sunglasses.
The shop is organizing a private sale and there will be 20 participants. Peter is assigned to take care of those
participants who says that they do not have any sunglasses.
(a) What is the probability that a participant does not have any sunglasses?
(b) Most likely, how many participants in the private sale do not have any sunglasses? Calculate the
probability of its happening.
(c) Peter is asking for an assistant for the private sales. His application should be approved if the probability
that there will be more than 4 participants in the private sale have no sunglasses is higher than 0.8.
Would his application be approved? Explain your answer with calculation.
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
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.
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