Assume that in a given year the mean mathematics SAT score was 495, and the standard deviation 111. A sample of 61 score is chosen. ANSWER ALL QUESTIONS PLEASE SHOW WORK A.What is the probability that same mean score is less than 484? B. The probability that the sample mean score is between 460 and 500 is? C. The 10th percentile of the sample mean is D. Would it be unusual if the sample mean were greater than 520? And what is the probability? E. Do you think it would be unusual for an individual to get a score greater than 520? What is the probability

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 + ...