QUESTION THREE (a) The daily sales of a product in different shops follow a normal distribution. The targeted mean of the daily sales of the product and their variance in the population are K10,000 and K2,500 respectively. The sales manager of the company which produces the product feels that the sales of the product has improved in the recent past. A random sample of 49 shops is taken from the normal population for which the mean daily sales is found to be K9,600. Check whether the sales of the product in different shops has really improved at a significance level of 0.05. (b) The weight of cement bags produced in a cement company follow normal distribution whose population is infinite. The expected mean of weight of the cement bags for sales of this population is 45KG and its variance is unknown. The sales manager of the firm claims that the mean weight of the cement bags is significantly more than the expected mean weight of the population. So, he has selected a random sample of 36 bags and its mean and variance are found to be 44KG and 1.25KG, respectively. Verify the intuition of the sales manager at a significance level of 0.05. (c) The quality manager of a washing machine company feels that the mean time between failures of the motors received is at most 90 days. The quality manager wants to test his intuition. Hence, he has taken a sample of 25 motors whose mean time between failure and its variance are found to be 93 days and 16 days, respectively. Verify the intuition of the quality manager at a significance level of 0.05