a) what is the mean?\nb) what is the median?\nc) what is the mode?\nd) what is the standard deviation?

Explanation:

Step1: Recall properties of normal - distribution

For a normal distribution, the mean, median, and mode are equal and located at the center of the distribution.

Step2: Identify the center value

The center of the given normal - distribution curve is at 55. So, mean = 55, median = 55, mode = 55.

Step3: Recall relationship for standard - deviation

In a normal distribution, if we assume that the points at which the curvature changes (inflection points) are approximately one standard - deviation away from the mean. The inflection points seem to be at 45 and 65. Using the formula $\text{mean}\pm\sigma$, where $\text{mean} = 55$. If $\text{mean}-\sigma=45$ and $\text{mean}+\sigma = 65$, then $\sigma=10$.

Answer:

a) 55 b) 55 c) 55 d) 10