Question

draw the graph of a normal curve with mean 45 and standard deviation 8

Explanation:

Step1: Recall normal - curve properties

A normal curve is symmetric about the mean $\mu$. Here $\mu = 45$. The points of inflection are at $\mu\pm\sigma$, where $\sigma = 8$. So the points of inflection are at $45 - 8=37$ and $45 + 8 = 53$.

Step2: Analyze the x - axis values

We usually mark values at $\mu - 3\sigma,\mu - 2\sigma,\mu-\sigma,\mu,\mu+\sigma,\mu + 2\sigma,\mu+3\sigma$.
$\mu-3\sigma=45-3\times8=45 - 24 = 21$.
$\mu - 2\sigma=45-2\times8=45 - 16 = 29$.
$\mu-\sigma=45 - 8=37$.
$\mu = 45$.
$\mu+\sigma=45 + 8=53$.
$\mu + 2\sigma=45+2\times8=45 + 16 = 61$.
$\mu+3\sigma=45+3\times8=45 + 24 = 69$.

Answer:

The correct graph should have the peak at $x = 45$ (the mean), and points of inflection at $x = 37$ and $x = 53$. The values on the x - axis should be symmetrically spaced around 45 with intervals of 8 for the standard - deviation increments. Among the given options, the graph with values $29,33,37,41,45,49,53,57,61$ on the x - axis is correct as it has the mean at 45 and the correct spacing based on the standard deviation of 8. So the answer is the second graph.