In each case, determine whether the situation calls for a
discrete or continuous random variable and explain
your answer.
a. The description of the number of children in a family
selected at random from families in Ft. Wayne, Indiana
b. The net worth of an average person in the United
States
c. The cholesterol level of individuals having heart
attacks between the ages of 35 and 50
d. The sum showing after a roll of two dice
a. The situation calls for a discrete random variable. This is because the number of children in a family can only take on certain specific values, such as 0, 1, 2, 3, and so on. It cannot take on any value between these whole numbers. Therefore, the variable is discrete.
To determine the number of children in a family selected at random from families in Ft. Wayne, Indiana, you would need to collect data from a random sample of families in the area and count the number of children in each family.
b. The situation calls for a continuous random variable. This is because net worth can take on a wide range of values, including decimals and fractions. It can vary continuously between different amounts. Therefore, the variable is continuous.
To determine the net worth of an average person in the United States, you would need to collect data from a representative sample of individuals and calculate their net worth, which includes assets minus liabilities.
c. The situation calls for a continuous random variable. This is because cholesterol level can be measured on a continuum, such as 150 mg/dL, 175 mg/dL, 200 mg/dL, and so on. It can have any value within a certain range. Therefore, the variable is continuous.
To determine the cholesterol level of individuals having heart attacks between the ages of 35 and 50, you would need to collect data from individuals who have had heart attacks within that age range and measure their cholesterol levels using laboratory tests.
d. The situation calls for a discrete random variable. This is because the sum of two dice can only take on specific values, such as 2, 3, 4, 5, and so on up to 12. It cannot take on any value between these whole numbers. Therefore, the variable is discrete.
To determine the sum showing after a roll of two dice, you would need to roll two dice many times and record the sum that appears on each roll. By repeating this process, you can gather data and determine the probabilities associated with each possible sum.