Question

the graph represents the distribution of the number of questions answered correctly on a 50 - question math test. what is the standard deviation of the data? 4 8 12 24

Explanation:

Step1: Recall property of normal - distribution

In a normal - distribution, approximately 68% of the data lies within 1 standard deviation of the mean, 95% within 2 standard deviations, and 99.7% within 3 standard deviations. If we assume the mean is around 36 (the peak of the normal - distribution curve) and we know that about 68% of the data lies in the interval \([\mu-\sigma,\mu + \sigma]\). Looking at the graph, if we assume the mean \(\mu = 36\), and we note that the interval from 32 to 40 seems to capture about 68% of the data.

Step2: Calculate the standard deviation

If \(\mu-\sigma=32\) and \(\mu = 36\), then \(36-\sigma=32\), so \(\sigma = 4\). Also, if \(\mu+\sigma = 40\) and \(\mu = 36\), then \(36+\sigma=40\), which also gives \(\sigma = 4\).

Answer:

A. 4