Question

the graph of a normal curve is given. use the graph to identify the value of μ and σ. the value of μ is □. the value of σ is □.

Explanation:

Step1: Recall the property of the mean ($\mu$) in a normal distribution

In a normal distribution, the mean ($\mu$) is the value at the center of the curve. Looking at the graph, the center value is $530$. So, $\mu = 530$.

Step2: Recall the property of the standard deviation ($\sigma$) in a normal distribution

The distance from the mean ($\mu$) to the inflection point (where the curve changes its concavity) is equal to the standard deviation ($\sigma$). The inflection point is at $515$ (or $545$). Using $\mu-\sigma$ formula: $\sigma=\mu - 515$. Substituting $\mu = 530$, we get $\sigma=530 - 515=15$.

Answer:

The value of $\mu$ is $530$ and the value of $\sigma$ is $15$.