Question 2 (a) The number of Camcoders sold in a week in a local shop, X, has the following probability distribution. Camcorders sold, x 0 2 4 5 6 Probability, P(X x) 0.05 0.12 0.19 3c 2c 0.10 0.04 (i) Find the value of c. (2 marks) (ii) Calculate the mean and standard deviation of X. (4 marks)(b) (c) (d) Assume thatthe number of customers visiting a new hair saloon follows a Poisson distribution with mean 5 visits in any 2-hour interval. (i) If the saloon operates 10 hours in a day, nd the number customers would be expected. (1 mark) (ii) Find the probability that the saloon will have at most 2 customer visits in rst 2 hours of the saloon opening. (3 marks) The time taken by the milkman to deliver to a school is normally distributed with a mean of 12 minutes and a standard deviation of 2 minutes. He delivers milk everyday. Find the probability that in a particular day, the milkman will take (i) less than 14 minutes to deliver the milk to school, (3 marks) (ii) between '9 and 13 minutes to deliver the milk to the school. (4 marks) A car service center is interested to investigate the relationship between the age of car (it, in years) and the cost of maintenance 0:, in RM) for a particular popular car model. The manager randomly selected eight cars that recently sent for maintenance. The following information on the ages and maintenance cost of these Age (years), it 7 3 5 S 2 6 3 Cost [Rh-0,): 1,530 450 780 1,680 320 1,260 390 (i) Determine the least square regression equation. (5 marks) (ii) Estimate the cost of maintenance of a 4-year-old car. Comment on the reliability of the estimate