Answered: A manufacturer produces humidifiers…

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 manufacturer produces humidifiers that have a mean life of at least 18000 hours when the production process is working properly. Based on past experience, it is known that the population standard deviation is 800 hours and the distribution of the service lives of the humidifiers is normal. The operations manager selects a random sample of 800 humidifiers, and the mean life of humidifiers is recorded.

a. Suppose the population mean life is 18000 hours. What is the probability that the sample mean life will be between 18050 and 17950 hours? Keep at least 4 decimal places.

Probability is:

b. Suppose the population mean life is 18000 hours. Based on a random sample of 800 humidifiers, there is a 5% chance that the mean life of humidifiers will be above..

_____ hours

use excel and the formula

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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