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Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 13PPS

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The combined SAT scores for the students at a local high school are normally distributed with a mean of 1462 and a standard deviation of 297. The local college includes a minimum score of 1759 in its admission requirements.

What percentage of students from this school earn scores that satisfy the admission requirement?

P(X > 1759) = ________ %

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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Let X denote the combined SAT scores for the students at a local high school and it follows normal distribution with a mean of $μ =$ 1462 and a standard deviation of $σ =$ 297.

Consider that the local college includes a minimum score of 1759 in its admission requirements.

The percentage of students from this school earn scores that satisfy the admission requirement is,

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