The scores of students on the SAT college entrance examinations at a certain high school had a normal distribution with mean μ=531.7μ=531.7 and standard deviation σ=29.2σ=29.2. (a) What is the probability that a single student randomly chosen from all those taking the test scores 536 or higher? ANSWER:  For parts (b) through (d), consider a simple random sample (SRS) of 30 students who took the test. (b) What are the mean and standard deviation of the sample mean score x¯x¯, of 30 students? The mean of the sampling distribution for x¯x¯ is:  The standard deviation of the sampling distribution for x¯x¯ is:  (c) What z-score corresponds to the mean score x¯x¯ of 536? ANSWER:  (d) What is the probability that the mean score x¯x¯ of these students is 536 or higher? ANSWER:

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 + ...