Answered: Suppose a team of biologists has been…

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

Suppose a team of biologists has been studying a fishing pond. Let x represent the length of a single trout taken at random from the pond. This group of biologists has determined that x (trout length) has a normal distribution with mean (mu) 10.5 inches and standard deviation (sigma) 1.2 inches. Use calculator command (normalcdf) to find your answer. Show your work by writing the command and numbers that you input. Round your answer to 4 decimal places.

What is the probability that the length of a single trout taken at random from the pond is between 7 and 11 inches long?
What is the probability that the mean length of five trout taken at random is between 7 and 11 inches?

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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