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?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...