Answered: A company produces breakfast cereal.…

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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A company produces breakfast cereal. The true mean weight of the contents of its cereal packages is 20 ounces, and the standard deviation is 0.6 ounce. The population distribution of weights is normal. Suppose that you purchase four packages, which can be regarded as a random sample of all those produced.
a. What is the standard error of the sample mean weight?
b. What is the probability that, on average, the contents of these four packages will weigh fewer than 19.7 ounces?
c. What is the probability that, on average, the contents of these four packages will weigh more than 20.6 ounces?
d. What is the probability that, on average, the contents of these four packages will weigh between 19.5 and 20.5 ounces?
e. Two of the four boxes are chosen at random. What is the probability that the average contents of these two packages will weigh between 19.5 and 20.5 ounces?

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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