Answered: A normal population has a mean of $66…

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 normal population has a mean of $66 and standard deviation of $18. You select random samples of nine.

Required:

a. Apply the central limit theorem to describe the sampling distribution of the sample mean with n = 9. With the small sample size, what condition is necessary to apply the central limit theorem?

b. What is the standard error of the sampling distribution of sample means? (Round your answer to 2 decimal places.)

c. What is the probability that a sample mean is greater than $69? (Round z-value to 2 decimal places and final answer to 4 decimal places.)

d. What is the probability that a sample mean is less than $62? (Round z-value to 2 decimal places and final answer to 4 decimal places.)

e. What is the probability that a sample mean is between $62 and $69? (Round z-value to 2 decimal places and final answer to 4 decimal places.)

f. What is the probability that the sampling error (x−μ)x-μ would be $9 or more? That is, what is the probability that the estimate of the population mean is less than $57 or more than $75? (Round z-value to 2 decimal places and final answer to 4 decimal places.)

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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