Question

the graph below shows the experimental probability of a runner finishing in first place (1), in second place (2), in third place (3), or not placing (4). which of the following describes the probability distribution?

(chart: bar graph titled finishing place with x - axis categories 1, 2, 3, 4 and y - axis labeled probability with values from 0 to 0.8. the bars for 1, 2, 3 are short, and the bar for 4 is tall.)

options:

• constant
• symmetric
• negatively skewed
• positively skewed

Explanation:

Step1: Recall Skewness Definitions

A negatively skewed distribution has a long tail on the left (low values), and a positively skewed distribution has a long tail on the right (high values). A symmetric distribution is balanced, and constant would mean all probabilities are equal.

Step2: Analyze the Bar Graph

• For finishing place 1, 2, 3: probabilities are low (short bars).
• For finishing place 4: probability is high (tall bar).
• The "tail" of low - probability values is on the left (places 1, 2, 3), and the high - probability value is on the right (place 4). This matches the definition of a negatively skewed distribution (long left tail). Wait, no—wait, negatively skewed: mean < median < mode, tail on left. Wait, in the graph, the highest bar (mode) is on the right (place 4), and the lower bars are on the left. So the tail is on the left (low values), so it's negatively skewed? Wait, no, maybe I mixed up. Let's re - define:

• Positively skewed: The tail is on the right (higher values have lower probabilities, tail extends to right).
• Negatively skewed: The tail is on the left (lower values have lower probabilities, tail extends to left).

In the given bar graph, the probabilities for lower finishing places (1, 2, 3) are low (tail on the left), and the probability for the highest finishing place category (4, not placing) is high. So this is a negatively skewed distribution? Wait, no, the options have "negatively skewed" and "positively skewed". Wait, maybe I made a mistake. Wait, let's look at the bars:

• Place 1: short bar (low probability)
• Place 2: short bar
• Place 3: short bar
• Place 4: tall bar

So the distribution has a long tail on the left (towards lower place numbers, which have low probabilities) and the peak (mode) on the right. So this is a negatively skewed distribution? Wait, no, the formula for skewness: if the tail is on the left, it's negative skewness. So the correct description is negatively skewed? Wait, but let's check the options again. The options are constant, symmetric, negatively skewed, positively skewed.

Wait, maybe I had it reversed. Let's think of the direction of the tail. In a positively skewed distribution, the tail is on the positive (right) side. In a negatively skewed, tail on the negative (left) side. So in this case, the low - probability values are on the left (places 1, 2, 3), so the tail is on the left, so it's negatively skewed.

Answer:

negatively skewed (the option corresponding to "negatively skewed" among the given radio buttons)