Answered: A random variable is not normally…

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

A random variable is not normally distributed, but it is mound shaped. It has a mean of 18 and a standard deviation of 2.

If you take a sample of size 12, can you say what the shape of the sampling distribution for the sample mean is? Why?

If the sample size is 12, then you can say the sampling distribution of the sample mean is not normally distributed since the sample size is less than 30.
If the sample size is 12, then you can't say anything about the sampling distribution of the sample mean, since the population of the random variable is not normally distributed and the sample size is less than 30.
If the sample size is 12, then you can say the sampling distribution of the sample mean is normally distributed since the sample size is less than 30.

For a sample of size 12, state the mean of the sample mean and the standard deviation of the sample mean. Round to two decimal places if necessary.
μ_x̄ =
σ_x̄ =

If you take a sample of size 36, can you say what the shape of the distribution of the sample mean is? Why?

If the sample size is 36, then you can say the sampling distribution of the sample mean is not normally distributed since the sample size is greater than 30.
If the sample size is 36, then you can say the sampling distribution of the sample mean is normally distributed since the sample size is greater than 30.
If the sample size is 36, then you can't say anything about the sampling distribution of the sample mean, since the population of the random variable is not normally distributed and the sample size is greater than 30.

For a sample of size 36, state the mean of the sample mean and the standard deviation of the sample mean. Round to two decimal places if necessary.
μ_x̄ =
σ_x̄ =

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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