The board of examiners that administers the real estate brokers’ examination in a certain state found that the mean score on the test was 435 and the standard deviation was 72.  Assume the scores are normally distributed.   (a) If the board wants to set the passing score so that only the best 30% of all applicants pass, what should be the passing score?   Z-value = Answer  (3 dp)    Passing Score Answer   (b)  What are the minimum and maximum scores of the middle 75% of persons that take the exam?   Min Z-value Answer (2 dp) Max Z-value Answer (2 dp) Min Exam Score Answer  Max Exam Score 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 + ...