Question

how to read normal graphs: look at the graphs shown below and choose the best match for the population mean μ and standard deviation σ. graph a has choose graph b has choose graph c has choose

Explanation:

Step1: Recall normal - distribution properties

The mean $\mu$ of a normal distribution is the center of the bell - shaped curve. The standard deviation $\sigma$ affects the spread of the curve. A smaller $\sigma$ gives a taller and narrower curve, while a larger $\sigma$ gives a shorter and wider curve.

Step2: Analyze Graph A

Graph A is centered around 6. So, $\mu = 6$. It is relatively wide, so it has a larger standard deviation. Let's assume $\sigma=2$.

Step3: Analyze Graph B

Graph B is centered around 10. So, $\mu = 10$. It is relatively narrow, so it has a smaller standard deviation. Let's assume $\sigma = 1$.

Step4: Analyze Graph C

Graph C is centered around 14. So, $\mu=14$. It has a moderate spread, so let's assume $\sigma = 1.5$.

Answer:

Graph A: $\mu = 6,\sigma = 2$; Graph B: $\mu = 10,\sigma = 1$; Graph C: $\mu = 14,\sigma = 1.5$