Question

hows 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 the mean

From the graph, the mean is at \(x = 0.5\), so the statement "The mean of the data is greater than \(0.5\)" is false.

Step2: Analyze the standard deviation

Assume the standard deviation \(s\). If we consider the normal - distribution - like curve (approximate). The distance from the mean \(x = 0.5\) to \(x=0.7\) is \(0.7 - 0.5=0.2\). If \(s = 0.1\), then \(0.7\) is \(2\) standard deviations from the mean (\(0.7-0.5 = 2s\) if \(s = 0.1\)), so the statement "A value of \(0.7\) is within \(1\) standard deviation of the mean" is false.
If \(s=0.1\), the data range for \(x=\mu\pm2s\) is \(0.5\pm0.2=(0.3,0.7)\). A value of \(0.9\) satisfies \(0.9-0.5 = 0.4=4s\) (if \(s = 0.1\)), which is more than \(2\) standard deviations from the mean.

Answer:

A value of \(0.9\) is more than \(2\) standard deviations from the mean.