The mean of Y is $19.35. The correct answer is option A.
Interpretation: If many, many ferry trips are randomly selected, the average amount of money collected on each trip would be approximately $19.35. This means that over a large number of trips, the expected amount of money collected per trip would be around $19.35.
The mean of a probability distribution is a measure of the average value of the random variable. To find the mean, we multiply each value of the random variable by its corresponding probability, and then sum up these products.
In this case, the random variable Y represents the money collected on a randomly selected ferry trip. The given probability distribution for Y is:
Money collected: 0 5 10 15 20 25
Probability: 0.02 0.05 0.08 0.16 0.27 0.42
To find the mean of Y, we multiply each value of Y by its corresponding probability and then sum up these products:
Mean (μY) = (0 * 0.02) + (5 * 0.05) + (10 * 0.08) + (15 * 0.16) + (20 * 0.27) + (25 * 0.42)
Mean (μY) = 0 + 0.25 + 0.8 + 2.4 + 5.4 + 10.5
Mean (μY) = 19.35
Therefore, the mean of Y is $19.35.
Interpretation: If many, many ferry trips are randomly selected, the average amount of money collected on each trip would be approximately $19.35. This means that over a large number of trips, the expected amount of money collected per trip would be around $19.35.