Question

which statement must be true? each distribution has the same mean and the same standard deviation. each distribution has the same mean and a different standard deviation. each distribution has a different mean and the same standard deviation. each distribution has a different mean and a different standard deviation.

Explanation:

Step1: Analyze Mean

In a normal distribution, the mean is the center (peak's x - value). The three curves have peaks at different x - values (red is leftmost, then green, then blue), so means are different.

Step2: Analyze Standard Deviation

Standard deviation relates to spread. The red curve is narrowest, blue is widest, green is in - between. So spreads (standard deviations) are different.

Answer:

Each distribution has a different mean and a different standard deviation.