QUESTION 2 a) The number of defective mobile phone in a batch of production is given by the following distribution.

Number of defective, y P(Y=v) Determine the value of w.

0 2w

1 0.25

2 0.14

3 0.11

4 w-0.1

i.

(3 marks) ii. Find the expected number of defective mobile phone for the production batch. (2 marks) iii. Find (3Y + 4) (2 marks) b) WeFix company has received three complaints on average due to the mobile phone malfunction per month. By assuming that the number of customer complaints follows a Poisson distribution, find the probability that at most five complaints will be received on January 2020. (3 marks) c) The internet is an alternative place to search for information for a project or piece of homework. In a survey, 35% students said that they used the internet for their homework. i. Find the probability at least eight out of ten of them use the internet for their homework. (2 marks) ii. Find the probability at least one out of seven of them do not use the internet for their homework. (3 marks)