Two companies, A and B, produce phones in country X. The number of phones produced by A is twice the number of phones produced by B.

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(a) Two companies, A and B, produce phones in country X. The number of phones produced by A is twice the number of phones produced by B. We know that 9% of phones produced by A and 10% of phones produced by B are faulty. Given that a randomly selected phone from X is faulty, find the probability that it was produced by B. [3 marks]

(b) The waiting time for processing of a refund by company B has an exponential distribution with mean of 100 days. Given that a customer has been already waiting for 120 days for their refund, find the average remaining waiting time. [2 marks]

(c) Use the Central Limit Theorem to approximate the probability that in a batch of randomly selected 1000 phones from X, no more than 80 are faulty. [4 marks]

 

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