You may need to use the appropriate appendix table or technology to answer this question. After deducting grants based on need, the average cost to attend the University of Southern California (USC) is $27,175. Assume the population standard deviation is $7,400. Suppose that a random sample of 52 USC students will be taken from this population. (a) What is the value of the standard error of the mean? (Round your answer to the nearest whole number.) $  (b) What is the probability that the sample mean will be more than $27,175?   (c) What is the probability that the sample mean will be within $1,000 of the population mean? (Round your answer to four decimal places.)   (d) What is the probability that the sample mean will be within $1,000 of the population mean if the sample size were increased to 100? (Round your answer to four decimal places.)

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 + ...