Answered: The weights of a certain brand of…

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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The weights of a certain brand of candies are normally distributed with a mean weight of 0.8563 g and a standard deviation of 0.052 g. A sample of these candies came from a package containing 456 candies, and the package label stated that the net weight is 389.7 g. (If every package has 456 candies, the mean weight of the candies must exceed StartFraction 389.7 Over 456 EndFraction equals0.8545 g for the net contents to weigh at least 389.7 g.) a. If 1 candy is randomly selected, find the probability that it weighs more than 0.8545 g. The probability is nothing. (Round to four decimal places as needed.) b. If 456 candies are randomly selected, find the probability that their mean weight is at least 0.8545 g. The probability that a sample of 456 candies will have a mean of 0.8545 g or greater is nothing. (Round to four decimal places as needed.) c. Given these results, does it seem that the candy company is providing consumers with the amount claimed on the label? ▼ Yes, No, because the probability of getting a sample mean of 0.8545 g or greater when 456 candies are selected ▼ is is not exceptionally small.

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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