The margarita is one of the most common tequila-based cocktails, made with tequila mixed with triple sec and lime or lemon juice, often served with salt on the glass rim. a common ratio for a margarita is 2: 1: 1, which includes 50% tequila, 25% triple sec, and 25% fresh lime or lemon juice. a manager at a local bar is concerned that the bartender uses incorrect proportions in more than 50% of margaritas. the manager secretly observes the bartender and finds that the bartender used the correct proportions in only 10 out of 30 margaritas. use the critical value approach to test if the manager’s suspicion is justified at α = 0.05. let p represent the population proportion of incorrectly made margaritas.

Aproduction line has three machines a, b, and c, with reliabilities of .96, .86, and .85, respectively. the machines are arranged so that if one breaks down, the others must shut down. engineers are weighing two alternative designs for increasing the line’s reliability. plan 1 involves adding an identical backup line, and plan 2 involves providing a backup for each machine. in either case, three machines (a, b, and c) would be used with reliabilities equal to the original three. a. compute overall system reliability under plan 1. (round your intermediate calculations and final answer to 4 decimal places.) reliability b. compute overall system reliability under plan 2. (round your intermediate calculations and final answer to 4 decimal places.) reliability c. which plan will provide the higher reliability? plan2plan1