Moatoga Company Ltd makes coffee tables. They believe that the tables need 80mL of varnish on average. A random sample of 200 similar coffee tables show that, on average, they have required 84 mL of varnish, with standard deviation of 4.5 mL. The sample standard deviation here is good estimate of the population standard deviation.

a)Calculate 95% confidence interval for the mean amount of varnish required for this type of coffee

b)On basis of this confidence interval explain whether the company's belief that the mean amount of varnish needed is 80 mL is correct.