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

Answer:

a. The percentage of bone density scores that are significantly high is    2.28​%.  

b. The percentage of bone density scores that are significantly low is  2.28​%.  

c. The percentage of bone density scores that are not significant is    95.45​%.

Step-by-step explanation:

Answer 2

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%.