Question

First photo question-The graph below shows three different normal distributions.

Answer 1

Answer:

For the first question:  They must each have a different mean and a different standard deviation.  For the second question:  In an observational study the researchers do not control treatment and in an experiment they do.  For the third question:  The second graph.  For the fourth question:  The second graph.

Step-by-step explanation:

For the first question:  We can see that each bell-shaped curve is centered around a different number.  This tells us that their means are all different.

We can also see that each curve has a different width; this means that the spread of data, measured in part by the standard deviation, is different as well.  This means both the mean and the standard deviation of each distribution is different.

For the second question:  In an observational study, as the name implies, all that is done is observation.  There is no treatment given by the researchers.  In an experiment, however, one group receives treatment and one group does not, so the differences can be measured.

For the third question:  In the first graph, the probabilities add up to 1.2.  This is more than 100%, so this is not a valid distribution.  In the second graph, the probabilities add up to 1.0; this is 100% exactly, so this is a valid distribution.

For the fourth question:  In the first graph, the probabilities only add up to 0.9.  This is not 100%, so this is not a valid distribution.  In the second graph, the probabilities add up to 1.0; this is 100% exactly, so this is a valid distribution.

Answer 2

First Question:
The statement that must be true is:
Each distribution has a different mean and a different standard deviation.

In a normal distribution, the mean is at the center of the graph. For these graphs, the middles are all different. 
The standard deviation is determined by the width of each graph. Again, the widths are all different.