The average length of messages received at a message...

The average length of messages received at a message switching center is 50 characters with a standard deviation of 10 characters. How many bytes (characters) of storage should be provided for each message buffer to ensure that $95 \%$ of all messages fit into one buffer?

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Key Concepts

Normal Distribution

A probability distribution that is symmetric about its mean, characterized by a bell-shaped curve where most values cluster around the average and the likelihood of outcomes decreases as they deviate further from the mean. It provides a framework for calculating the probability of a variable falling within a particular range, which is essential for determining thresholds such as the 95th percentile.

Z-score

A standardized value that expresses the number of standard deviations a data point is from the mean. Z-scores allow for the comparison of data from different normal distributions and are used to determine the probability corresponding to a particular value, which helps in setting criteria like the necessary buffer size.

Percentiles

A measure indicating the value below which a given percentage of observations in a dataset fall. In applied contexts, selecting a specific percentile (such as the 95th percentile) ensures that the vast majority of cases are covered, facilitating decisions like determining sufficient storage capacity for message buffers.

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