FRQ #1: The manager of a local fast-food restaurant is concerned about *customers who ask for a water cup when placing an order but fill the cupwith a soft drink from the beverage fountain instead of filling the cup withwater. The manager selected a random sample of 80 customers whoasked for a water cup when placing an order and found that 23 of thosecustomers filled the cup with a soft drink from the beverage fountain.a) Construct and interpret a 95 percent confidenceinterval for the proportion of all customers who, having asked for a watercup when placing an order, will fill the cup with a soft drink from thebeverage fountain.b) The manager estimates thateach customer who asks for a water cup but fills it with a soft drink coststhe restaurant $0.25. Suppose that in the month of June 3,000 customersask for a water cup when placing an order. Use the confidence intervalconstructed in part (a) to give an interval estimate for the cost to therestaurant for the month of June from the customers who ask for a watercup but fill the cup with a soft drink.

1) Given,Sample size, n = 80Number of successes in sample, x = 23(a) Given, confidence level = 95% = 0.95So level of significance, α = 1-0.95 = 0.05At α = 0.05, the critical value is, Zc = 1.96 (Using Excel function = 1.96)Now,Sample proportion , Therefore, 95% confidence interval is= (0.18832, 0.38668)Interpretation:- We are 95% confident that the proportion of all customers who, having asked for a water cup when placing an order, will fill the cup with a soft drink from the beverage fountain is between 0.18832 and 0.38668.(b) Given,The manager estimates that each customer who asks for a water cup but fills it with a soft drink costs the restaurant $0.25.In the month of June 3,000 customers ask for a water cup when placing an order.The interval estimate for the cost to the restaurant for the month of June from the customers who ask for a water cup but fill the cup with a soft drink is= ($141.24 , $290.01)(a) The 95% confidence interval is (0.18832 , 0.38668)Interpretation:- We are 95% confident that the proportion of all customers who, having asked for a water cup when placing an order, will fill the cup with a soft drink from the beverage fountain is between 0.18832 and 0.38668.(b) The interval estimate for the cost to the restaurant for the month of June from the customers who ask for a water cup but fill the cup with a soft drink is ($141.24 , $290.01)