In a small town, a computer store sells laptops to the local...

In a small town, a computer store sells laptops to the local residents. However, due to low demand, they like to keep their stock at a manageable level. The data they have indicate that the weekly demand for the laptops they sell follows the distribution given in the table below. (TABLE CANNOT COPY) a) Find the mean and standard deviation of this distribution. b) Use the empirical rule to find the approximate number of laptops that is sold about $95 \%$ of the time.

In a small town, a computer store sells laptops to the local residents. However, due to low demand, they like to keep their stock at a manageable level. The data they have indicate that the weekly demand for the laptops they sell follows the distribution given in the table below.
(TABLE CANNOT COPY)
a) Find the mean and standard deviation of this distribution.
b) Use the empirical rule to find the approximate number of laptops that is sold about $95 \%$ of the time.

Key Concepts

Probability Distribution

A probability distribution describes how the probabilities are distributed over the values of a random variable. In the context of demand data, it specifies the likelihood associated with each possible amount of demand, forming the basis for calculating other statistics such as the mean and standard deviation.

Mean of a Distribution

The mean, or expected value, of a distribution is a measure of central tendency that represents the average outcome. It is computed by multiplying each possible value by its respective probability and summing these products. The mean provides a central reference point for the distribution of values.

Standard Deviation

The standard deviation is a measure of the dispersion or spread of values around the mean. It quantifies how much the values typically deviate from the average. In many applications, including demand forecasting, understanding the variability is key for planning and risk management.

Empirical Rule

The empirical rule, also known as the 68-95-99.7 rule, is a guideline that applies to distributions that approximate a normal distribution. It states that about 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. This rule helps approximate the range in which the majority of observations are likely to occur.

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