3. In studying the efficiency of the federal court system, we look at the random variable, X, the amount of time elapsing between the filing of a charge and the trial date. A random sample of n = 86 cases yields a sample mean of 11.4 months, with sample variance s2x = 5.8 months.

(a) Find a 90% confidence interval on the average time between the filing of charges and the date of trial.
(b) Find a 95% confidence interval on ¦Ìx.
(c) What is the probability that a case would require at least one year between the filing of charges and the date of trial?

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