A certain access method, called method A, has been found to...

A certain access method, called method $A$, has been found to give a mean record retrieval time of 36 milliseconds with a standard deviation of 7 milliseconds, while method $B$ has a mean retrieval time of 42 milliseconds with a standard deviation of 4 milliseconds. (a) If a major design objective is to have $90 \%$ of all individual retrievals completed in 55 milliseconds or less, which method should be selected? (b) Does the chosen method meet the objective?

A certain access method, called method $A$, has been found to give a mean record retrieval time of 36 milliseconds with a standard deviation of 7 milliseconds, while method $B$ has a mean retrieval time of 42 milliseconds with a standard deviation of 4 milliseconds.
(a) If a major design objective is to have $90 \%$ of all individual retrievals completed in 55 milliseconds or less, which method should be selected?
(b) Does the chosen method meet the objective?

Key Concepts

Percentile Evaluation

Percentile evaluation involves determining the value below which a given percentage of observations in a group fall. It is used to ensure that a specified proportion of all retrieval times meet a design target, such as having at least 90% of retrievals completed within a set time limit.

Z-Score

The Z-score is a standardized measure that expresses the number of standard deviations an individual value is from the mean. In problems dealing with performance thresholds, computing the Z-score allows for the estimation of the probability that an observation falls below or above a certain value.

Mean

The mean is the measure of central tendency that provides the average value of a dataset. In the context of retrieval times, the mean indicates the typical time it takes to retrieve a record, serving as a benchmark for comparing different methods.

Standard Deviation

The standard deviation measures the amount of variation or dispersion around the mean. It tells us how spread out the individual retrieval times are, which is crucial when ensuring that a high percentage of operations meet a prescribed time threshold.

Normal Distribution

The normal distribution is a continuous probability distribution that is symmetric about its mean. When retrieval times follow a normal distribution, properties like percentiles and probabilities can be accurately determined using standard statistical methods, which is essential when verifying design objectives.

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