Question

c. yes, the graph fulfills the properties of the normal distribution. the mean is approximately 20 and the standard deviation is about
(type whole numbers.)

Explanation:

Step1: Recall the empirical rule of normal distribution

In a normal distribution, about 68% of the data lies within 1 standard deviation of the mean, 95% within 2 standard deviations, and 99.7% within 3 standard deviations.

Step2: Estimate the range for 1 - standard - deviation

The mean is approximately \( \mu = 20 \). If we assume that the points where the curvature of the normal curve changes (inflection points) are at \( \mu\pm\sigma \). Looking at the graph, if we assume that the inflection points are around \( x = 15 \) and \( x = 25 \) (a rough estimate from the scale on the x - axis).
Using the formula \( \mu+\sigma=x_{2} \) and \( \mu - \sigma=x_{1} \), substituting \( \mu = 20 \), \( x_{1}=15 \), \( x_{2}=25 \)
From \( \mu+\sigma=x_{2} \), we have \( 20+\sigma = 25 \), so \( \sigma=5 \)
Or from \( \mu - \sigma=x_{1} \), \( 20-\sigma=15 \), so \( \sigma = 5 \)

Answer:

5