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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Question

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?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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