the graph represents the distribution of the number of questions answered correctly on a 50 - question math…
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? math test scores 4 8 12 24
Answer
Explanation:
Step1: Recall normal - distribution property
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 curve) and we know that one standard - deviation out from the mean on either side contains about 68% of the data. Looking at the graph, if we consider the interval from 32 to 40 (a common estimate for the range within 1 standard - deviation of the mean for a normal distribution centered around 36), we can calculate the standard deviation.
Step2: Calculate standard deviation
The formula for the range within 1 standard - deviation of the mean is $\mu\pm\sigma$, where $\mu$ is the mean and $\sigma$ is the standard deviation. If $\mu = 36$ and the lower bound of the 1 - standard - deviation interval is 32, then $36-\sigma=32$ (or if we consider the upper bound $36 + \sigma=40$). Solving for $\sigma$ gives $\sigma=4$.
Answer:
4