Answered: Describe in your own words what the…

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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Describe in your own words what the Central Limit Theorem does for us.

5.If it is known that the mean time between eruptions at Old Faithful is 96 minutes with a standard deviation of 12 minutes, answer the following.

a)Hailey only has 70 minutes left in the park today, what is the chance that she will still see an eruption if she only just missed the last one?

b)Park rangers gather a sample of 45 random eruptions. Describe the sampling distribution that results. Center:Spread: Shape:

c)What is the probability that the mean of this sample of 45 is more than 100 minutes?

d)What is the probability that the mean of this sample differs from the true mean by more than 2 minutes?

e)What would be an unusually large mean wait time based on this distribution?

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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