State of economy Probability of state of Stock A Rate of return Stock B Rate of return economy 0.3 Recession Normal Boom 10% -10% 0.3 15% 25% 12% 0.4 15% Based on the above information calculate for stock A and B: (a) (b) Expected return (3 marks) Variance Standard deviation (3 marks) (d) (3 marks) (c) Give your comment on the standard deviation of both stocks (1 mark) 4.A recent survey shows that 60% of the factory workers willing to work overtime without extra pay as long as they are guaranteed job security and bonus at the end of the year. Fifteen factory workers are randomly selected, find (Use binomial formula): (a) The mean and standard deviation of the number of workers who are willing to work overtime without extra pay. (2 marks) (b) The probability that at least 13 workers are willing to work overtime without extra pay. (3 marks) (c)The probability that 10 workers are unwilling to work overtime without extra pay. (2 marks) (d) Explain why a binomial distribution is suitable for computing probabilities of the number of workers who are willing to work overtime without pay. (3 marks) State of economy Probability of state of Stock A Rate of return Stock B Rate of return economy 0.3 Recession Normal Boom 10% -10% 0.3 15% 25% 12% 0.4 15% Based on the above information calculate for stock A and B: (a) (b) Expected return (3 marks) Variance Standard deviation (3 marks) (d) (3 marks) (c) Give your comment on the standard deviation of both stocks (1 mark) 4.A recent survey shows that 60% of the factory workers willing to work overtime without extra pay as long as they are guaranteed job security and bonus at the end of the year. Fifteen factory workers are randomly selected, find (Use binomial formula): (a) The mean and standard deviation of the number of workers who are willing to work overtime without extra pay. (2 marks) (b) The probability that at least 13 workers are willing to work overtime without extra pay. (3 marks) (c)The probability that 10 workers are unwilling to work overtime without extra pay. (2 marks) (d) Explain why a binomial distribution is suitable for computing probabilities of the number of workers who are willing to work overtime without pay