Pls help ASAP. Tyvm

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 I. (3 marks) (b) Find an approximation to the distribution of the sample mean 7,, of a large random sample (size n = 30) of 7 (5 marks) (c) For a particular sample of size 50, t = 2.4. Find a 95% confidence interval for (7 marks) (d) Assume a - 10, compute the smallest sample size required if we wish to be 95% confident that the sample mean T, is within 1 0.5 of the true mean