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?

finishing place

constant
symmetric
negatively skewed
positively skewed

Explanation:

Analyze the shape of the distribution

Using the Skewed Distribution Properties knowledge point, we observe the heights of the bars across the values on the horizontal axis \(x\):

• At \(x = 1\), the probability is very low (\(0.05\)).
• At \(x = 2\), the probability is \(0.10\).
• At \(x = 3\), the probability is \(0.15\).
• At \(x = 4\), the probability is very high (\(0.70\)).

The data values are concentrated on the right side (high values), while a long tail extends to the left toward the lower values.

Determine the direction of skewness

Using the Skewed Left knowledge point:

• A distribution with a long tail on the left side is described as skewed left or negatively skewed.
• Conversely, a distribution with a long tail on the right side is described as skewed right or positively skewed.
• Since the tail of this probability distribution points toward the left (negative direction), it is negatively skewed.

Answer:

• constant
• symmetric
• negatively skewed (Correct answer)
• positively skewed