1. List four properties of the student's distribution. [4 Marks] 2. Mwangaza limited deals in the production of electronic bulbs. A random sample of 10 electronic bulbs produced by the company yielded the following results on the lifetime of the bulbs. Lifetime(hours) 4,400 4,800 3,700 3,900 5,500 4,000 3,700 4,100 4,000 5,400 Required: Test at a 5% per cent level of significance, whether there is a significant difference between the sample mean and the population mean. [6 Marks] 3. Suppose that a random sample of 100 students is selected to estimate the average amount of fees arrears. The sample mean is Ksh. 54,000 with a standard deviation of Ksh. 25,000. Calculate: (i) A 95% confidence interval for the mean. [3 Marks] (ii) The sample size that would be required to estimate the mean to within 200 with a 95% confidence level. [3 Marks] 4. The number of tasks sent to an office printer per minute follows a Poisson distribution with a parameter 30 . Using the normal approximation to the Poisson distribution, find the probability that in one minute there are more than 35 tasks. [4 Mar