Question

based on the graph above, which statement best describes the graph?
answer
the two distributions have means that differ by 4 units and different standard deviations.
the two distributions have means and standard deviations that differ by 4 units.
the two distributions have means that differ by 4 units and equal standard deviations.
the two distributions have equal means and equal standard deviations.

Explanation:

Step1: Analyze the graph's characteristics

The graph shows two distributions. The spread (related to standard deviation) seems different as the curves have different widths. The positions (related to mean) differ by \(12 - 8=4\) units.

Step2: Evaluate each option

• Option 1: "The two distributions have equal means and equal standard deviations" is wrong as means differ (\(12 - 8 = 4\)) and spreads (related to standard deviation) are different.
• Option 2: "The two distributions have means that differ by 4 units and equal standard deviations" is wrong as standard deviations (spreads) are different.
• Option 3: "The two distributions have means that differ by 4 units and different standard deviations" is correct as \(12-8 = 4\) (mean difference) and spreads (standard deviation - like characteristics) are different.
• Option 4: "The two distributions have equal means and equal standard deviations" is wrong as means differ (\(12 - 8=4\)).

Answer:

The two distributions have means that differ by 4 units and different standard deviations.