Question

the graph shows a distribution of data. which statement about the data is true? the data has a standard deviation of 0.1. the mean of the data is greater than 0.5. a value of 0.7 is within 1 standard deviation of the mean. a value of 0.9 is more than 2 standard deviations from the mean.

Explanation:

Step1: Analyze normal - distribution properties

In a normal distribution, the mean is at the center of the bell - shaped curve. Here, the center of the curve is around \(x = 0.5\).

Step2: Evaluate standard - deviation statements

Assume the mean \(\mu\approx0.5\). If the standard deviation \(\sigma = 0.1\), then the interval within 1 standard deviation of the mean is \([\mu-\sigma,\mu + \sigma]=[0.4,0.6]\), and within 2 standard deviations is \([\mu - 2\sigma,\mu+2\sigma]=[0.3,0.7]\).
A value of \(0.7\) is at the boundary of 2 standard deviations from the mean, not 1 standard deviation. A value of \(0.9\) is more than 2 standard deviations from the mean since \(\mu+2\sigma\approx0.5 + 2\times0.1=0.7\) and \(0.9>0.7\). Also, we cannot be sure that the standard deviation is \(0.1\) just from the graph, and the mean is around \(0.5\) not greater than \(0.5\).

Answer:

D. A value of 0.9 is more than 2 standard deviations from the mean.