3. The College Board reported the following mean scores for the three parts of the Scholastic Aptitude Test (SAT) (The World Almanac, 2009): Critical Reading465 Mathematics534 Writing 542 Assume that the population standard deviation on each part of the test is σ=100. 3a. What is the probability that a random sample of 100 test takers will provide a sample mean test score within 10 points of the population mean of 465 on the Critical Reading part of the testf?

Central limit theorem: The central limit theorem state that the sampling distribution of the sample…

Answered: 3. The College Board reported the…

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

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Chapter10: Statistics

Section10.4: Distributions Of Data

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3. The College Board reported the following mean scores for the three parts of the Scholastic Aptitude Test (SAT) (The World Almanac, 2009):
	Critical Reading	465
	Mathematics	534
	Writing		542
Assume that the population standard deviation on each part of the test is σ=100.

3a. What is the probability that a random sample of 100 test takers will provide a sample mean test score within 10 points of the population mean of 465 on the Critical Reading part of the testf?

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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