which statement must be true?\no each distribution has a different mean and the same standard deviation.\no…

which statement must be true?\no each distribution has a different mean and the same standard deviation.\no each distribution has a different mean and a different standard deviation.\no each distribution has the same mean and the same standard deviation.\no each distribution has the same mean and a different standard deviation.

which statement must be true?\no each distribution has a different mean and the same standard deviation.\no each distribution has a different mean and a different standard deviation.\no each distribution has the same mean and the same standard deviation.\no each distribution has the same mean and a different standard deviation.

Answer

Explanation:

Step1: Recall properties of normal - distribution curves

The mean of a normal - distribution is at the center of the curve (the peak). The standard deviation determines the spread of the curve.

Step2: Analyze the given curves

The peaks of the three normal - distribution curves are at the same x - value (around 70), so they have the same mean. The curves have different spreads; the blue curve is the narrowest (smallest standard deviation), and the red curve is the widest (largest standard deviation). So, they have different standard deviations.

Answer:

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