Answered: In 2005, 1,475,623 students heading to…

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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In 2005, 1,475,623 students heading to college took the SAT. The distribution of scores in the math section of the SAT follows a normal distribution with mean of 520 and a standard deviation of 115. Use this information to answer the next five questions.

What variable is being measured? Describe in words.

Calculate the z-score for an SAT score of 680. Round your answer to 2 decimal places.

If one student is randomly selected, find the probability that she has an SAT score of at least 700. Sketch a diagram of this normal distribution labeling the mean, the x-value and the area that represents the probability. Show and label all work.

What percentage of students have scores between 500 and 720? Round to 2 decimal places.

Enormous State University (ESU) will only accept students in the top 15% of SAT scores. What is the lowest SAT score you can have and be admitted to ESU? Round your answer to the nearest whole number.

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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