For bone density scores that are normally distributed with a mean of 0 and a standard deviation of 1, find the percentage of scores that are

a. significantly high (or at least 2 standard deviations above the mean).

b. significantly low (or at least 2 standard deviations below the mean).

c. not significant (or less than 2 standard deviations away from the mean).

In a normal distribution 68.27% of the values are within one standard deviation from the mean, 95.5% of the values are within two standard deviations from the mean, and 99.7 % of the values are within three standard deviations of the mean

With that you have the answer to the three questions:

a. significantly high (or at least 2 standard deviations above the mean).

99.5% of the values are within 2 standard deviations from the mean, half of 100% - 95.5% = 4.5% / 2 = 2.25% are above the mean, so the answer is 2.25%

b. significantly low (or at least 2 standard deviations below the mean).

The other half are below 2 standard deviations, so the answer is 2.25%

c. not significant (or less than 2 standard deviations away from the mean).

As said, 95.5% are within the band of two standard deviations from the mean, so the answer is 95.5%.