Answered: normal distribution with a mean μ=…

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 large population of male African Bush Elephants is to be sampled. The weights of the elephants in the population follow a normal distribution with a mean μ= 13,000 lbs and standard deviation σ = 3,200 lbs.

What is the z-score for a weight value 14,000 lbs in the population? Round your answer to two decimal places.

Using the answer from the previous question, find the probability the weight of a randomly selected elephant is less than 14,000 lbs. Keep four decimal places in your answer.

What is the probability the mean weight for a random sample of 16 elephants is less than 14,000 lbs? Keep four decimal places in your answer.

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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