Question

The average score of students on an anthropology test is 32, and the standard deviation is 3.5. For this normally distributed data, the probability of which range of scores is represented by the area of the shaded region of the given curve?
28.5 to 32
28.5 to 35.5
25 to 39
25 to 35.5
21.5 to 32

Answer 1

You will need to standardize your range values:
\[Z=\frac{X-\mu}{\sigma} \] where X is you given value, \(\mu\) is the mean (average), and \(\sigma\) is the standard deviation. Then you can use the standard normal table to find the appropriate probabilities.

Answer 2

i only have 2 numbers to work with so i'm lost

Answer 3

Oh ok it's a picture. So it looks like the area goes from the point \(\mu - 3\sigma\) to \(\mu\)

So... \(\mu = 32\) and \(\sigma = 3.5\)

So:
\(\mu - 3 \sigma = 32 - 3(3.5)= 21.5\)

So the area goes from 21.5 to 32.