The population mean and standard deviation are given below. Find the required probability and determine whether the given sample mean would be considered unusual. For a sample ofn=70,find the probability of a sample mean being greater than219ifμ=218andσ=5.8. For a sample ofn=70,the probability of a sample mean being greater than219ifμ=218andσ=5.8(Round to four decimal places as needed.)Would the given sample mean be considered unusual? The sample mean▼ wouldwould notbe considered unusual because it▼ liesdoes not liewithin the range of a usual event, namely within▼ 1 standard deviation2 standard deviations3 standard deviationsof the mean of the sample means.

the PDF of normal distribution is = 1/σ * √2π * e ^ -(x-u)^2/ 2σ^2standard normal distribution is a…

Answered: The population mean and standard…

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 population mean and standard deviation are given below. Find the required probability and determine whether the given sample mean would be considered unusual.

For a sample of

n=70,

find the probability of a sample mean being greater than

219

μ=218

and

σ=5.8.

For a sample of

n=70,

the probability of a sample mean being greater than

219

μ=218

and

σ=5.8

(Round to four decimal places as needed.)

Would the given sample mean be considered unusual?

The sample mean

▼

would

would not

be considered unusual because it

▼

lies

does not lie

within the range of a usual event, namely within

▼

1 standard deviation

2 standard deviations

3 standard deviations

of the mean of the sample means.

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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