Question

the graph shows a distribution of data with a standard deviation of 6. which statement is true about the data point 84? it is within 1 standard deviation of the mean. it is within 2 standard deviations of the mean. it is exactly 3 standard deviations from the mean. it is exactly 4 standard deviations from the mean.

Explanation:

Step1: Find the mean

From the graph, the mean \(\mu = 75\).

Step2: Calculate the number of standard deviations

Given standard deviation \(\sigma=6\). Let \(x = 84\). Use the formula \(z=\frac{x-\mu}{\sigma}\). Substitute \(x = 84\), \(\mu = 75\) and \(\sigma = 6\) into the formula: \(z=\frac{84 - 75}{6}=\frac{9}{6}=1.5\).

Since \(1<1.5<2\), the data point \(84\) is within \(2\) standard deviations of the mean.

Answer:

It is within 2 standard deviations of the mean.