Answered: An electric company has been selling a…

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

An electric company has been selling a bulb, which was advertised as having an average life of 1, 500 hours. Assume that the lifetime of these bulbs is normally distributed with a standard deviation of 800 hours. A random sample of 16 bulbs from this manufacturing process was tested ad their lifetimes were recorded.

a. What is the probability that the sample mean is between 1,250 and 1,750 hours?

b. A lot consisting of 10,000 bulbs will be rejected if the sample mean based on 16 bulbs is 1,200 hours or less.What is the probability that the lot will be rejected?

2. A manufacturer of a low-tar cigarette claims that its cigarettes contain an average of 16.3 mg. of tar with a standard deviation of 3.1 mg per cigarette. What is the probability that in a sample of 225 cigarettes, the sample mean (of tar in cigarette in mg.) is higher than 15.9?

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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