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PROBLEM 25.1 (pg 229, #52) The lifetime of a certain type of battery is normally distributed with mean 12 hours and standard deviation 2 hour. There are four batteries in a package. a. Determine the mean of T, or E[T. ]. b. Determine the variance of T. or Var [T.]. c. Determine the mean of X or E[X] d. Determine the variance of X or Var[X]. e. What lifetime value k is such that the total lifetime of all batteries in a package exceeds k 92% of the time? Thus we seek: P(T, > k) = 0.92 or P(X > k/4) =0.92 PROBLEM 25.2 Let X1.....Xeon denote the actual net weights of 400 randomly selected 50-lb bags of fertilizer. a. If the expected weight of each bag is 50 and the variance is 1, use the normal curve to approximate P(49.85