Q2 (61) An electrical firm manufacturing light bulbs that have a length of life that is normally distributed with a standard deviation of 5 hours. As an engineer, you want to estimate the mean lifespan of a certain light bulbs. (i) (ii) (iii) Determine the sample size needed if it will be 90% condent that the error will not exceed 2 hours when you use the sample mean as a point estimate for the true mean. (6 marks) If a sample of 30 bulbs were selected randomly and found to have an average of 120 hours. Let it be the population mean of life lengths of all bulbs manufactured by this rm. Produce the 90% condence interval of the mean lifespan of a certain light bulbs. [7 marks) You as the engineer are not satisfied with the confidence interval and want to do another study to find a shorter condence interval. What should you change? [2 marks)