A company produces batteries whose lifetimes are normally distributed with a mean of 100 hours. It is known that 96% of the batteries last at least 40 hours. Throughout this question all answers should be given correct to one decimal place. () If P(z > a) = 0.96, use normal distribution tables to find the value of 'a'. a = (b) Estimate the standard deviation lifetime. (c) Calculate the percentage of batteries that will last less than 57 hours. The company is liable to replace any battery which lasts for less than 40 hours. The company wishes to reduce the percentage of defective batteries from the current level of 4% to 2%. (d) (i) Use normal tables to find the value 'b' such that P(z < b) 2%. (ii) The company can use a chemical procedure which changes the values of the mean and standard deviation. If the standard deviation is set at 35 hours, find the mean lifetime which will reduce the percentage of defectives to 2%.