Question

A small ferry runs every half hour from one side of a large river to the other. The probability distribution for the random

variable Y = money collected (in dollars) on a randomly selected ferry trip is shown here.



Money collected 0 5 10 15 20 25

Probability 0.02 0.05 0.08 0.16 0.27 0.42



What is the mean of Y? Interpret this value.



μY - $19.35. If many, many ferry trips are randomly selected, the average amount of money collected would be about $19.35.

The mean cannot be calculated because we do not

know the sample size.

μY = $12.50. If many, many ferry trips are randomly selected, the amount of money collected would be

$12.50.

μY - $19.35. If many, many ferry trips are randomly selected, the amount of money collected would be

$19.35.

μY - $12.50. If many, many ferry trips are randomly selected, the average amount of money collected would be about $12.50.

Answer 1

The mean (expected value) of the random variable Y, representing money collected on ferry trips, is $19.35. In numerous random selections, the average amount collected would be around $19.35.

To find the mean (expected value) of a random variable Y, you multiply each possible value of Y by its corresponding probability and then sum up these products.

Mean (μY) = Σ (Y * P(Y))

Using the provided probability distribution:

μY = (0 * 0.02) + (5 * 0.05) + (10 * 0.08) + (15 * 0.16) + (20 * 0.27) + (25 * 0.42)

μY = 0 + 0.25 + 0.8 + 2.4 + 5.4 + 10.5

μY = 19.35

Therefore, the correct interpretation is:

μY = $19.35. If many, many ferry trips are randomly selected, the average amount of money collected would be about $19.35.