EXAMPLE 7Calculating the mean of a discrete probability distribution

Note: These 10 friends constitute a population, not a sample, so the mean is , not

Carla has 10 friends in school. She took a census of all 10 friends, asking each how many credits they had registered for that semester. Five of her friends were taking 15 credits, with one each taking 12, 13, 14, 16, and 20 credits. The relative frequency distribution is shown in Table 3.

Table 6.8: Table 3Relative frequency distribution for the number of credits
Credits Frequency Relative frequency
12 1 0.1
13 1 0.1
14 1 0.1
15 5 0.5
16 1 0.1
20 1 0.1
  1. Construct the probability distribution table for .
  2. Calculate the mean number of credits taken.

Solution

  1. Our random variable is . We use the relative frequencies from Table 3 to assign probabilities to the various values of . The resulting probability distribution table is shown in the first two columns of Table 4.

  2. To find the mean , we first need to multiply each possible outcome (value of ) by its probability . This is shown in the right-hand column in Table 4. We multiply the value by its probability , the value by its probability , and so on. Then we add these five products to find the mean:

    Table 6.9: Table 4Probability distribution table of
    12 0.1
    13 0.1
    14 0.1
    15 0.5
    16 0.1
    20 0.1
    Total 1.0

317

The mean number of credits taken by Carla's friends is 15.

NOW YOU CAN DO

Exercises 45a–52a.