Question 1 You are asked to perform some statistical analysis on a particular brand of television. After doing some research, you realised that the time, 7, it takes for this brand of television to spoil is uniformly distributed between 0 and a inclusive, where a is a positive constant. Answer the following questions and show full details of your workings. (a) Derive the mean and variance of T. ( b ) Find an approximation to the distribution of the sample mean In of a large random sample (size n > 30) of T. (c) For a particular sample of size 50, t = 2.4. Find a 95% confidence interval for CI. (d) Assume a = 10, compute the smallest sample size required if we wish to be 95% confident that the sample mean 7, is within 10.5 of the true mean