The mean time to retrieve a record from an online database is 222 milliseconds with a standard deviation of 62 milliseconds. The design criterion requires that at least 80% of all retrieval times must not differ from the mean by more than 83 milliseconds.Use Chebyshev's inequality to establish whether the design criterion is satisfied.Would the design criterion be satisfied if it were known that the retrieval time is normally distributed with a mean of 222 milliseconds and a standard deviation of 62 milliseconds?

Chebyshev's inequality is a probability inequality that states that for any random variable X, the…

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Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 31EQ

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The mean time to retrieve a record from an online database is 222 milliseconds with a standard deviation of 62 milliseconds. The design criterion requires that at least 80% of all retrieval times must not differ from the mean by more than 83 milliseconds.

Use Chebyshev's inequality to establish whether the design criterion is satisfied.
Would the design criterion be satisfied if it were known that the retrieval time is normally distributed with a mean of 222 milliseconds and a standard deviation of 62 milliseconds?

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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