Reference no: EM132173829

a) Among 25,000 machines, 3,000 have defective components. Of the 3000 ma- chines that have defective components, 2,500 have only minor defects and 500 have major defects. Determine the probability that a machine selected at random has major defects, given that it has defective components. 

b) The battery life of a particular brand of mobile phone is known to be normally distributed with a mean of 2.25 years and a standard deviation of 0.5 years.

(i) Find the probability that a randomly selected mobile phone of this brand will last at least 2 years but less than 3 years. 

(ii) Suppose a random sample of four such phones is selected. What is the probability that exactly three of them will last at least 2 years but less than 3 years? 

c) Defective medical devices can have serious consequences for users. A specific type of medical device, once manufactured, is tested and 3% of the devices are found to have defective parts. Let X = the number of medical devices with defective parts in a random sample of size n = 20. 

(iii) Determine the probability that 2 or more of the devices are defective. 

(iv) Determine the probability that between 1 and 4 (inclusive) devices are defective.