The average life of a radio battery brand is 35 hours. The distribution of the average lifetimes of these batteries is approximately normal, with a variance of 30.25 hours2. As part of the testing program, the manufacturer inspects a batch of 400 batteries, of which it takes samples of size 25. a) What is the standard error of the distribution of the sample mean?b) What percentage of the sample means will have an error of ± 3 hours from the batch mean?c) What percentage of samples will have a half-life greater than 34.5 hours?d) How many samples will have a mean shelf life greater than 34.5 and less than 36 hours?

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