Question

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).

Answer 1

a) Scores of 2 and higher are significantly high

b) Scores of -2 and lower are significantly low

c) Scores between -2 and 2 are not significant.

Explanation:

Mean = 0

Standard deviation = 1

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

2 standard deviations above the mean is:

0 + 1*2 = 2

So scores of 2 and higher are significantly high

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

2 standard deviations below the mean is:

0 - 1*2 = -2

So scores of -2 and lower are significantly low

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

2 standard deviations above the mean is:

0 + 1*2 = 2

2 standard deviations below the mean is:

0 - 1*2 = -2

So scores between -2 and 2 are not significant.