A normal distribution of scores has a mean of 72 and a standard deviation of 11. Find the z-scores corresponding to each of the following values: A score that is 20 points above the mean. A score that is 10 points below the mean. A score that is 15 points above the mean A score that is 30 points below the mean. A fifth grader takes a standardized achievement test (mean = 115, standard deviation = 10) and scores a 148. What is the child’s percentile rank? Three students take equivalent stress tests. Which is the highest relative score (meaning which has the largest z score value)? A score of 144 on a test with a mean of 130 and a standard deviation of 34. A score of 90 on a test with a mean of 85 and a standard deviation of 18. A score of 18 on a test with a mean of 21 and a standard deviation of 5.

Problem 1:Given:μ = mean = 72σ = standard deviation = 11 We can solve for z-scores using this…

Answered: A normal distribution of scores has a…

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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A normal distribution of scores has a mean of 72 and a standard deviation of 11. Find the z-scores corresponding to each of the following values:

A score that is 20 points above the mean.

A score that is 10 points below the mean.

A score that is 15 points above the mean

A score that is 30 points below the mean.

A fifth grader takes a standardized achievement test (mean = 115, standard deviation = 10) and scores a 148. What is the child’s percentile rank?

Three students take equivalent stress tests. Which is the highest relative score (meaning which has the largest z score value)?

A score of 144 on a test with a mean of 130 and a standard deviation of 34.

A score of 90 on a test with a mean of 85 and a standard deviation of 18.

A score of 18 on a test with a mean of 21 and a standard deviation of 5.

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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