This image presents a question involving the percentage of bone density scores that fall under different categories based on their relationship to the mean of a normal distribution. Let me break it down:

1. Mean and Standard Deviation: The scores are normally distributed with a mean of 0 and a standard deviation of 1. This means it follows the standard normal distribution.

2. Question Breakdown:

   • Part a asks for the percentage of scores that are at least 2 standard deviations above the mean (significantly high).
   • Part b asks for the percentage of scores that are at least 2 standard deviations below the mean (significantly low).
   • Part c asks for the percentage of scores that are within 2 standard deviations of the mean (not significant).

To answer these, we can use the empirical rule (or 68-95-99.7 rule) for a normal distribution:

• Approximately 95% of the data falls within 2 standard deviations of the mean.
• This leaves 5% of the data outside of 2 standard deviations.
  • 2.5% will be below 2 standard deviations (significantly low).
  • 2.5% will be above 2 standard deviations (significantly high).

Solutions:

a. Percentage of scores significantly high (above 2 standard deviations): 2.5%
b. Percentage of scores significantly low (below 2 standard deviations): 2.5%
c. Percentage of scores that are not significant (within 2 standard deviations): 95%

Would you like further details on the calculations or normal distribution concepts?

Here are some related questions for further understanding:

1. What is the significance of a Z-score in the context of normal distribution?
2. How does the empirical rule apply to non-standard normal distributions?
3. What percentage of data falls within 1 standard deviation of the mean?
4. Can you explain the concept of "tails" in a normal distribution?
5. How would these percentages change if we considered 3 standard deviations instead of 2?

Tip: For normally distributed data, Z-scores can help easily determine how extreme a particular score is relative to the rest of the distribution.