Answered: (c) the percent of observations that…

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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NOTE: The numerical values in this problem have been modified for testing purposes.

Suppose composite scores on the ACT test for the high school graduating class in a certain year had mean 20.9 and standard deviation 5.3. In all, 1,799,243 students in this class took the test. Of these, 170,777 had scores higher than 28 and another 54,167 had scores exactly 28 . ACT scores are always whole numbers. The exactly Normal N (20.9,5.3) distribution can include any value, not just whole numbers. What is more, there is no area exactly above 28 under the smooth Normal curve. So ACT scores can be only approximately Normal.

(c) the percent of observations that are greater than 28 using the N(20.9, 5.3) distribution. (The percent greater than or
equal to 28 is the same, because there is no area exactly over 28.) (Enter your answer rounded to two decimal places.)
percent:
%

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 + ...

Expert Solution

Step 1

Here we calculate the percentage by using central limit theorem.

The formula is,

$z = \frac{x - μ}{σ}$

were,

$μ$ : Population mean.

$σ$ : Population standard deviation.

Given,

$P o p u l a t i o n m e a n = μ = 20.9 P o p u l a t i o n s \tan d a r d d e v i a t i o n = σ = 5.3$

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