Answered: n a large high school of 2500 students,…

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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Question

n a large high school of 2500 students, the mean number of cars owned by students’ families is 2.35 with a standard deviation of 1.06 cars.

a) Think about this distribution. Do you think it is normal? Using the empirical rule give the ranges for each of the 3 standard deviations assuming this is a symmetric and mound shaped distribution. Does it seem like this is the distribution is normal?

b) A simple random sample of 16 students is taken and the mean number of cars owned is calculated. What are the mean and standard deviation of the sample mean? Can we use this to find probabilities? Why or why not?

c) A simple random sample of 36 students is taken and the mean number of cars owned is calculated. What are the mean and standard deviation of the sample mean? Can we use this to find probabilities? Why or why not?

d) Using the information in part c) What is the probability that the sample mean is greater than 2.5 cars? Insert the graph from Rguroo that gives the output for this question.

2) In a large high school of 2500 students, 21% of them are seniors.

a) A simple random sample of 150 students is taken and the proportion of seniors is calculated. What are the mean and standard deviation of the sample proportion? Can we use this to calculate probabilities? (That is does it meet the assumptions of the Central Limit Theorem?)

b) What is the probability that the sample will contain less than 15% seniors? Insert the graph from Rguroo that gives the output for this question.

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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