Answered: A biologist studies the gestation…

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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A biologist studies the gestation period of wolves. Past data reveals that such gestation periods have a mean of 65 days with standard deviation 20 days. The normal distribution for the population is shown by the dotted black line.

The biologist plans to take a random sample of 15 such wolves and will calculate the mean gestation period of the sample to compare to the known gestation periods. Compute the mean and standard deviation of the sampling distribution of sample means for a sample of size 15. Round your answers to the nearest tenth.

Show your answer by moving the two draggable points to build the sampling distribution.

Provide your answer below:

$$μx=50

$$σx =6.1

The population has a normal distribution

with mean 65 and standard deviation 6.1

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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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