The home states of a certain group of people are distributed as follows: 54 percent are from MISSOURI, 27 percent are from KANSAS, and 19 percent are from IOWA. (No one in the group had a home state other than one of these three.)
(Note: Your answer to the question below should be rounded to three decimal places.)
Suppose we randomly select a person from this group. What is the expected value of the number of letters in the selected person's home state?
To find the expected value of the number of letters in the selected person's home state, we need to calculate the weighted average of the number of letters in each state based on their respective probabilities.
First, we need to determine the number of letters in each state:
- MISSOURI has 8 letters.
- KANSAS has 6 letters.
- IOWA has 4 letters.
Next, we calculate the expected value:
Expected value = (probability of MISSOURI * number of letters in MISSOURI) + (probability of KANSAS * number of letters in KANSAS) + (probability of IOWA * number of letters in IOWA)
Expected value = (0.54 * 8) + (0.27 * 6) + (0.19 * 4)
Expected value = 4.32 + 1.62 + 0.76
Expected value ≈ 6.70
Therefore, the expected value of the number of letters in the selected person's home state is approximately 6.70.