[10 marks] Tess Productions is a curator of ambient funky and stylish home environments and a magazine is interested including her as a feature article. To be accepted in the magazine then it must be statistically proven and achieve an average score above 85 points. The distribution of the ratings is approximately Normal with a known standard deviation of 10 points. (a) (6 marks) Tess takes a sample of 30 design ratings with a mean rating of 90 points and standard deviation of 10 points. Construct and interpret a 99% confidence interval to estimate Tess's population average rating score on her designs. (b) (2 marks) Does Tess's average score achieve her a place in the article? (C) (2 marks) Does the population have to be Normally distributed here? Explain briefly