Statistics

C3I. For an audio retail shop, there is a 10% chance that an incoming customer would make a
purchase before he/she leaves the shop.
a) What is the probability distribution for the number of customers who make a
purchase before he/she leaves the shop? Explain briefly. (3 marks)
b) In a given day, 40 customers visited the shop.
i) What is the probability that 3 customers made purchases? (3 marks)
ii) What is the probability that not less than 3 customers made purchases?
(4 marks)
II. A manufacturer produces packets of sweets with a mean weight of 200 grams and a variance
of 25 grams. It is believed that the weights of the packets are normally distributed.
a) What is the probability that a packet of sweets weights between 195 grams and 205
grams? (4.5 marks)
b) What are the probabilities that a packet of sweet is less than 140 grams
(1.5 marks)
c) In the quality control process, the bottom 13% of packets are classified as
underweighted and are rejected, what is the minimum weight of packet that passes the
weight requirement? (4 marks)