An investigator polls a representative sample of common cold sufferers, asking them to estimate the number of hours of physical discomfort caused by their most recent cold. Their estimates approximate a normal curve with a mean of 91 hours and a standard deviation of 23 hours. Show your z-score and p-value calculations. (1) Inverse Normal Distribution: What is the estimated number of hours for the shortest-suffering 20 percent?(1) Inverse Normal Distribution: A medical researcher wishes to concentrate on the 10 percent who suffered the most. To be included in this group, a patient would have suffered how many hours?

Given : An estimates approximate a normal curve with a mean of 91 hours and a standard deviation of 23 hours. Population Mean μ = 91 Standard Deviation σ = 23A) X be the random variable follows Normal distribution. X ~ N ( μ = 91 ,σ = 23 ) Here Z =(X - μ)/σ Now p(Z < z)= 0.20 p(Z< -0.842 )= 0.20 i.e z= -0.842 Excel formula NORM.INV(0.20,0,1) By using z score formula x = μ + zσ = 91 + -0.842 x 23 = 71.63 the estimated number of hours for the shortest-suffering 20 percent is 71.63B) p(Z > z)= 0.10 p(Z> 1.282 )= 0.10 i.e z= 1.282 Excel formula: =1-NORM.S.INV(0.10) from z score formula x = μ + zσ = 91 + 1.282 x 23 = 120.49 A patient would have suffered 120.49 hours

Answered: An investigator polls a representative…

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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An investigator polls a representative sample of common cold sufferers, asking them to estimate the number of hours of physical discomfort caused by their most recent cold. Their estimates approximate a normal curve with a mean of 91 hours and a standard deviation of 23 hours. Show your z-score and p-value calculations.
(1) Inverse Normal Distribution: What is the estimated number of hours for the shortest-suffering 20 percent?
(1) Inverse Normal Distribution: A medical researcher wishes to concentrate on the 10 percent who suffered the most. To be included in this group, a patient would have suffered how many hours?

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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