B1 (a) A LED lamp manufacturer produces a batch of 5W LED lamp with a mean lifetime of 35,000 hours and a standard deviation of 1500 hours. Assuming that the lifetime of LED lamp is normally distributed. (i) Find the probability that one of these LED lamps with (4 marks) lifetime greater than 38,000 hours. (ii) Find the percentage of LED lamps expected with a lifetime (4 marks) between 33,500 and 36,500 hours. (iii) The lifetime of a LED lamp shall not be less than 32,000 (4 marks) hours referring to the quality standard of this manufacturer. Determine the number of 5W LED lamp(s) that will be rejected in a production batch of 10,000. (b) A new product of 20W LED lamp is under development and the probability of a 20W LED lamp get failed in the laboratory test is 0.1. 50 pieces of the prototype are selected randomly for laboratory test, calculate the probability that: (i) none of LED lamps failed; (2 marks) (ii) exactly three of LED lamps failed; and (2 marks) (iii) more than three LED lamps failed. (4 marks)