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

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

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

Answer

Explanation:

Step1: Understand normal - distribution properties

The peak of a normal - distribution curve represents the mean. Since the peaks of the three curves are at the same x - value (around 70), they have the same mean.

Step2: Analyze spread of curves

The spread of a normal - distribution curve is determined by the standard deviation. A smaller standard deviation results in a narrower curve, and a larger standard deviation results in a wider curve. The three curves have different widths, so they have different standard deviations.

Answer:

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