Math / Data & Statistics

QuestionOne graph in the figure represents a normal distribution with mean $\mu=13$ and standard deviation $\sigma=3$ . The other graph represents a normal distribution with mean $\mu=6$ and standard deviation $\sigma=3$ . Determine which graph is which and explain how you know.
Choose the correct answer below. A. Graph A has a mean of $\mu=13$ and graph B has a mean of $\mu=6$ because a larger mean shifts the graph to the left. B. Graph $A$ has a mean of $\mu=6$ and graph $B$ has a mean of $\mu=13$ because a larger mean shifts the graph to the right. C. Graph A has a mean of $\mu=13$ and graph $B$ has a mean of $\mu=6$ because a larger mean shifts the graph to the right. D. Graph A has a mean of $\mu=6$ and graph B has a mean of $\mu=13$ because a larger mean shifts the graph to the left.

Studdy Solution

STEP 1

1. We have two normal distribution graphs, one with mean $\mu=13$ and the other with mean $\mu=6$ .
2. Both graphs have the same standard deviation $\sigma=3$ .
3. A normal distribution is centered around its mean.

STEP 2

1. Understand the effect of the mean on the position of a normal distribution graph.
2. Identify which graph corresponds to which mean based on their positions.

STEP 3

The mean of a normal distribution determines the center of the graph. A larger mean shifts the graph to the right on the horizontal axis.

STEP 4

Given that graph A is centered around 6 and graph B is centered around 13, identify the graphs based on their centers.
The correct answer is:
C. Graph A has a mean of $\mu=13$ and graph B has a mean of $\mu=6$ because a larger mean shifts the graph to the right.

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