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Percentage conversion is a vital step in many statistical calculations. It's all about transforming a percentage into a decimal to make mathematical operations easier.

In our example, we start with a percentage value, specifically 2%. To convert this percentage into a decimal, we need to divide by 100. This is because a percentage is simply a fraction out of 100.

So, taking the 2% from the problem, divide it by 100 to get 0.02.

This decimal representation is crucial for the later steps, such as multiplication, which will enable you to find out the expected values and other statistical metrics.

Expected value is a fundamental concept in probability and statistics. It gives you an idea of what to anticipate on average from a random process. For this exercise, you want to know the average number of gifts the college can expect based on the number of solicitations.

To compute the expected value, you multiply the number of trials (solicitations) by the probability of a successful outcome (receiving a gift).

The formula to use here is:

• Expected Number of Gifts = Total Solicitations \( \times \) Probability

Plugging in the values from the problem, the total solicitations are 2,000, and the probability of a gift is 0.02. Therefore, the calculation is:

\( 2000 \times 0.02 = 40 \).

This means that, on average, the college can expect 40 gifts for every 2,000 solicitations.

Statistical calculations often involve multiple steps, using both basic arithmetic and understanding of probability principles. In this example, we combined percentage conversion with the expected value calculation.

Performing these calculations requires attention to detail to ensure accuracy, which is crucial for achieving correct results.

The steps are:

• Convert percentages to decimals for easier calculations.
• Apply the expected value formula to predict average outcomes.
• Verify results through straightforward multiplication.

Each step logically leads to the next, showcasing the interconnectedness of statistical methods. This process helps to not only solve problems but also develop a deeper understanding of statistical concepts.