A district sales manager for a franchise fast-food company wants to determine the average sales of a burger that they recently introduced. In a random sample of 30 locations, the average daily sales was found to be $5420 with a standard deviation of $510.

a. Calculate the margin of error for a 90% confidence interval for the average sales of the burger that they recently introduced.

b. Construct the 90% confidence interval for the average sales of the burger that they recently introduced.

c. Interpret the interval in part b.

d. How large of a sample size is necessary to reduce the 90% margin of error to $120?