Using a Frequency Distribution to Find Probabilities In Exercises 49-52, use the frequency distribution at the left, which shows the population of the United States by age group, to find the probability that a U.S. resident chosen at random is in the age range. (Source: U.S. Census Bureau)
52. 65 years old and older

Verified step by step guidance

1. Step 1: Understand the problem. We are tasked with finding the probability that a randomly chosen U.S. resident is 65 years old or older. To do this, we need to use the frequency distribution table provided.
2. Step 2: Identify the relevant data. From the table, the frequency for the age group '65 and over' is 54.1 million. The total population is the sum of all frequencies in the table.
3. Step 3: Calculate the total population. Add the frequencies for all age groups: 73.0 + 30.2 + 87.6 + 83.3 + 54.1. This gives the total population in millions.
4. Step 4: Use the formula for probability. The probability of a U.S. resident being 65 years old or older is given by the formula: P(65 and over) = (Frequency of 65 and over) / (Total population).
5. Step 5: Simplify the fraction. Divide the frequency for '65 and over' (54.1 million) by the total population calculated in Step 3 to find the probability. Express the result as a decimal or percentage.

Key Concepts

Frequency Distribution

A frequency distribution is a summary of how often each value occurs in a dataset. It organizes data into categories (or bins) and shows the number of observations (frequency) for each category. In this case, the frequency distribution presents the population of the U.S. by age group, allowing for easy visualization of how many people fall into each age category.

Probability

Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. In the context of the question, it involves calculating the probability that a randomly selected U.S. resident belongs to a specific age group, which can be determined by dividing the frequency of that age group by the total population.

Total Population

The total population refers to the sum of all individuals in the dataset being analyzed. To find the probability of a resident being in a specific age group, one must first calculate the total population by summing the frequencies of all age groups. This total serves as the denominator in the probability calculation, providing a context for the relative size of each age group.