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. μY = $19.35.

Money collected 0 5 10 15 20 25
Probability 0.02 0.05 0.08 0.16 0.07 0.42





Compare the mean and the median. Based upon the relationship between the mean and the median, what is the shape of the probability distribution?



The probability distribution is skewed to the right. This relationship makes sense because the mean of Y is less than the median of Y.



The probability distribution is skewed to the right. This relationship makes sense because the mean of Y is greater than the median of Y.



The probability distribution is symmetric. This relationship makes sense bocause the mean of Y is less than the median of Y.



The probability distribution is skewed to the left. This relationship makes sense because the mean of Y is less than the median of Y.



The probability distribution is skewed to the left. This relationship makes sense because the mean of Y is greater than

the median of Y.

Answer 1

The probability distribution for the random variable Y, which represents the money collected on a randomly selected ferry trip, is given as:

Money collected: 0, 5, 10, 15, 20, 25 dollars

Probability: 0.02, 0.05, 0.08, 0.16, 0.07, 0.42

To find the mean or expected value of Y (μY), we multiply each money amount by its corresponding probability and sum up the results.

(0 * 0.02) + (5 * 0.05) + (10 * 0.08) + (15 * 0.16) + (20 * 0.07) + (25 * 0.42) = 19.35 dollars

Therefore, the mean (expected value) of the money collected on a randomly selected ferry trip is $19.35.

This means that on average, the ferry collects $19.35 per trip.

It's important to note that the mean is a measure of central tendency that provides a typical value, but it may not represent any actual amount collected on a specific trip.

Step-by-step explanation:

Answer 2

The probability distribution is skewed to the right. This relationship makes sense because the mean of Y is less than the median of Y.

Step-by-step explanation:

The relationship between the mean and the median can help determine the shape of a probability distribution. In this case, the mean of $19.35 is less than the median. Since the mean is pulled towards the tail, the probability distribution is skewed to the right.