Answered: (Previous exam question). A wine…

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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2. (Previous exam question). A wine producer is trying to decide if it is time to harvest his grapes. He sends out two of his pickers to collect several bunches of grapes in order to measure the sugar content of each bunch. If the mean sugar content of both the first and the second picker's bunches exceeds 24.0oBRIX, the producer will harvest, otherwise he will wait. The first picker collects 50 bunches and the second picker collects 100 bunches. The bunches are chosen randomly and independently. If the true mean sugar content of all grape bunches in the vineyard is 23.75oBRIX with a variance of .781, what is the probability that the harvest will begin? Answer: 2. .0000524

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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