Q6 The following table shows the probability distribution of the number of mobile phones per family in Hong Kong. These figures were collected by a local telecommunications company. Number of mobile 2 4 5 6 phones per family 3 Probability 0.08 0.22 0.46 0.12 0.1 0.02 (a) Calculate the expected number of mobile phones per family. (2 marks) (b) The counting of mobile phones from a large batch of families contains 5% errors. If 10 families are randomly selected from the batch, find the probability that () no errors were found (2 marks) (ii) no more than 4 errors were found (3 marks) (c) Suppose the family members report to the telecommunications company follow a Poisson distribution at an average of 8 per day. Find the probability that no more than 3 family members report on the coming day. (3 marks) Q7 The scores on a TOEFL examination have a mean of 520 and a standard deviation of 35. Assume the scores are normally distributed. (a) If the top 10% of students who take the examination are selected, find the cutoff score. (5 marks) (b) What is the probability that a randomly selected student will score between 590 and 600? (3 marks) Q8 The weight of local tertiary students is normally distributed with mean 67 kg and standard deviation of 9 kg. Find the probability that (a) a randomly chosen student has a height of more than 65 kg. (3 marks) (b) a randomly chosen student has a height of less than 60 kg. (3 marks) (c) a randomly chosen student has a height between 60 kg. and 65 kg. (4 marks)