Suit Sales The number of suits sold per day at a retail...

Suit Sales The number of suits sold per day at a retail store is shown in the table, with the corresponding probabilities. Find the mean, variance, and standard deviation of the distribution. $$ \begin{array}{l|lllll}{\text { Number of suits sold } X} & {19} & {20} & {21} & {22} & {23} \\ \hline \text { Probability } P(X) & {0.2} & {0.2} & {0.3} & {0.2} & {0.1}\end{array} $$ If the manager of the retail store wants to be sure that he has enough suits for the next 5 days, how many should the manager purchase?

Suit Sales The number of suits sold per day at a retail
store is shown in the table, with the corresponding probabilities. Find the mean, variance, and standard deviation of the distribution.
$$
\begin{array}{l|lllll}{\text { Number of suits sold } X} & {19} & {20} & {21} & {22} & {23} \\ \hline \text { Probability } P(X) & {0.2} & {0.2} & {0.3} & {0.2} & {0.1}\end{array}
$$
If the manager of the retail store wants to be sure that he
has enough suits for the next 5 days, how many should
the manager purchase?

Key Concepts

Central Limit Theorem

The Central Limit Theorem states that the sum (or average) of a large number of independent, identically distributed random variables tends toward a normal distribution, regardless of the original distribution. This allows for approximating probabilities for the total sales over several days, which aids in determining a sufficient stock level.

Sum of Independent Random Variables

When independent random variables are summed, the mean of the total is the sum of the individual means, and the variance is the sum of the individual variances. This concept is used to calculate the total expected number of suits sold over multiple days.

Mean (Expected Value)

The mean, or expected value, of a random variable is the long?term average of its outcomes weighted by their probabilities. It represents the central or typical value of the distribution, and is found by summing each outcome multiplied by its probability.

Probability Distribution

A probability distribution assigns a probability to each possible outcome of a random variable. In this context, it specifies the likelihood of selling each number of suits per day, and it forms the basis for calculating the distribution’s mean and variance.

Variance and Standard Deviation

The variance measures the spread of a random variable’s outcomes around its mean, calculated as the weighted average of the squared deviations from the mean. The standard deviation is the square root of the variance, and it provides an indication of the typical deviation from the mean in the same units as the variable.

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