Answered: A manufacturer of compact fluorescent…

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 of compact fluorescent light bulbs advertises that the distribution of the lifespans of these light bulbs is nearly normal with a mean of 9,800 hours and a standard deviation of 950 hours.

(a) What is the probability that a randomly chosen light bulb lasts more than 10,500 hours?
__________________ (please round to four decimal places)

(b) Describe the distribution of the mean lifespan of 15 light bulbs. Refer to pages 172-173, box on 177, and 195.

__approximately normal with μ = 9800 and
__left skewed
__right skewed
__approximately normal with μ = 9800 and σ = 950

(c) What is the probability that the mean lifespan of 15 randomly chosen light bulbs is more than 10,500 hours? __________________ (please round to four 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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