SAT scores: Assume that in a given year the mean mathematics SAT score was 515, and the standard deviation was 116. A sample of 65 scores is chosen. Use Excel. (a) What is the probability that the sample mean score is less than 500?(b) What is the probability that the sample mean score is between 480 and 520? Round the answer to at least four decimal places.(c) Find the 80th percentile of the sample mean. Round the answer to at least two decimal places. (d) Would it be unusual if the sample mean were greater than 550? Round the answer to at least four decimal places.(e) Do you think it would be unusual for an individual to get a score greater than 550? Explain. Assume the variable is normally distributed. Round the answer to at least four decimal places.

Answered: (a) What is the probability that the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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SAT scores: Assume that in a given year the mean mathematics SAT score was 515, and the standard deviation was 116. A sample of 65 scores is chosen. Use Excel.

(a) What is the probability that the sample mean score is less than 500?

(b) What is the probability that the sample mean score is between 480 and 520? Round the answer to at least four decimal places.

(d) Would it be unusual if the sample mean were greater than 550? Round the answer to at least four decimal places.

(e) Do you think it would be unusual for an individual to get a score greater than 550? Explain. Assume the variable is normally distributed. Round the answer to at least 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 + ...

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