Answered: Tomatoes Agricultural scientists are…

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

Tomatoes Agricultural scientists are working on devel-
oping an improved variety of Roma tomatoes. Marketing

research indicates that customers are likely to bypass
Romas that weigh less than 70 grams. The current variety
of Roma plants produces fruit that averages 74 grams, but

11% of the tomatoes are too small. It is reasonable to as-
sume that a Normal model applies.

a) What is the standard deviation of the weights of Ro-
mas now being grown?

b) Scientists hope to reduce the frequency of undersized
tomatoes to no more than 4%. One way to accomplish

this is to raise the average size of the fruit. If the stan-
dard deviation remains the same, what target mean

should they have as a goal?
c) The researchers produce a new variety with a mean
weight of 75 grams, which meets the 4% goal. What
is the standard deviation of the weights of these new
Romas?

d) Based on their standard deviations, compare the toma-
toes produced by the two varieties.

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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