The manager of a pizza chain wants to determine the average size of their advertised 19 inch pizzas. she takes a random sample of 29 pizzas and records their mean and standard deviation as 19.10 inches and 1.2 inches, respectively. she subsequently computes 99% confidence interval of the mean size of all pizzas (18.53,19.67). however, she finds this interval to be too broad to implement quality control and decides to reestimate the mean based on a bigger sample. using the standard deviation estimate of 1.2 from her earlier analysis, how large a sample must she take if she wants the margin of error to be under 0.5 inch