100 similar machines each have 16 components that wear independently of each other. Let X; N Bin(16, p) for i : 1, . . . , 100 denote the random variable for the number of worn components for a machine after 20 days of continuous use. The total number of worn components is 2:3 23,; = 540. (a) Calculate an estimate for the probability that a component wears after 20 days, and provide an estimate of its standard error to 4 decimal places. Probability Estimate: Standard Error: (b) Calculate an approximate 95% condence interval for the population probability parameter 3). Give your answer to 2 decimal places. 95% Condence Interval: [- -)