Question 2 (a) A sample comprising of 300 respondents was surveyed to obtain information on how employees would react to pay freeze in view of the weak economic climate. Table 2 shows the information obtained. Accet Pa Freeze Re'ect Pa Freeze \" __ Table 2 (i) What is the probability that a respondent is a male or rejects a pay freeze? (0.75) (ii) What is the probability that a respondent accepts a pay freeze, given that the respondent chosen is a female? (0.5556) (iii) Are \"Accept Pay Freeze\" and \"Female" categories independent events? Explain your answer with workings. (b) 20% of the cars produced by a manufacturer are found to be defective. A sales representative received a shipment of 8 randomly selected cars from the manufacturer. (i) What is the probability that one car is defective? (0.3355) (ii) What is the probability that at least two cars are defective? (0.4967) (iii) Calculate the expected number of defective cars in this shipment and its variance. (1.28) (c) The life of a mobile phone battery \"Always Ready" is normally distributed with a mean of 18,000 hours and a standard deviation of 2,000 hours. (i) What percentage of the batteries will last between 15,000 hours and 23,000 hours? (92.7%) (ii) What percentage of the batteries will last at most 13,000 hours? (0.62%) (iii) What percentage of the batteries will last at least 30,000 hours? (0%) (iv) At most, how many hours will 85% of the batteries last? (20,080)