Question

For a normal distribution with mean of 80 and a standard deviation of 8, find the number of standard deviations the raw score 67 is from the mean (Give answer as a positive value rounded to nearest hundredth). 

Answer 1

(80 - 67) / 8

Answer 2

(67 - 80) / 8 = 13/8

Answer 3

[AI-generated answer — Explain Bot]

To find the number of standard deviations a raw score is from the mean, you can use the formula:

\(z = \frac{x - \mu}{\sigma}\)

where:
- \(z\) is the number of standard deviations
- \(x\) is the raw score
- \(\mu\) is the mean
- \(\sigma\) is the standard deviation

In this case, the raw score is 67, the mean is 80, and the standard deviation is 8.

\(z = \frac{67 - 80}{8}\)
\(z = \frac{-13}{8}\)
\(z = -1.625\)

Since we need to give the answer as a positive value, we can take the absolute value of \(z\), which gives:

\(z = 1.625\)

Rounding this to the nearest hundredth, we get:

\(z \approx 1.63\)

Therefore, the raw score 67 is approximately 1.63 standard deviations below the mean of 80.