The Great West Mining Company has struck the mother lode in their newly acquired gold field. They are modelling the weights of the gold nuggets they'll find over the next year using a normal distribution with a mean of228ozand a standard deviation of70oz.Use this table or the ALEKS calculator to find the percentage of nuggets that will be found over the next year weighing between319 oz and 347oz according to the model. For your intermediate computations, use four or more decimal places. Give your final answer to two decimal places (for example 98.23%).

From the provided information, Mean (µ) = 228 oz Standard deviation (σ) = 70 oz X~N (228, 70)The required percentage of nuggets that will be found over the next year weighing between 319 oz and 347 oz according to the model can be obtained as: P319<X<347=P319-22870<X-μσ<347-22870=P1.3<Z<1.7=PZ<1.7-PZ<1.3=0.955435-0.9032From excel =NORM.S.DIST(1.7,TRUE) and =NORM.S.DIST(1.3,TRUE)=0.052235≈5.22% The excel outputs are as follow: Thus, the required percentage is 5.22%.

Answered: The Great West Mining Company has…

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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The Great West Mining Company has struck the mother lode in their newly acquired gold field. They are modelling the weights of the gold nuggets they'll find over the next year using a normal distribution with a mean of

228

and a standard deviation of

Use this table or the ALEKS calculator to find the percentage of nuggets that will be found over the next year weighing between

319

and

347

according to the model. For your intermediate computations, use four or more decimal places. Give your final answer to two decimal places (for example

98.23%

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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