Answered: The size of fish is very important to…

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 size of fish is very important to commercial fishing. A study conducted in
2012 found the length of Atlantic cod caught in nets in Karlskrona to have a mean
of 49.9 cm and a standard deviation of 3.74 cm (Ovegard, Berndt & Lunneryd,
2012). The length of fish is normally distributed. A sample of 15 fish is taken.
a.) State the random variable.
b.) Find the mean of the sample mean.
c.) Find the standard deviation of the sample mean
d.) What is the distribution of the sample mean? Why?
e.) Find the probability that the sample mean length of the Atlantic cod is less
than 52 cm.
f.) Find the probability that the sample mean length of the Atlantic cod is more
than 74 cm.
g.) If you found sample mean length for Atlantic cod to be more than 74 cm, what
could you conclude?

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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