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).

a. The percentage of bone density scores that are significantly high is nothing​%. ​(Round to two decimal places as​ needed.)

Answer 1

Solution:

Given: The bone density scores that are normally distributed with a mean of 0 and a standard deviation of​ 1.

Since mean is 0 and standard deviation is 1, given Normal variate can be treated as Standard Normal variate.

That is: Z = The bone density scores ~ Standard Normal distribution ( Mean = 0 , Standard deviation = 1).

Part a) find the percentage of scores that are significantly high​ (or at least 2 standard deviations above the​ mean).

That is find:

Look in z table for z = 2.0 and 0.00 and find corresponding area.

P( Z< 2.00 ) = 0.9772

thus

Part b)  find the percentage of scores that are significantly low​ (or at least 2 standard deviations below the​ mean).

that is find:

Look in z table for z = -2.0 and 0.00 and find corresponding area.

P( Z< -2.00) = 0.0228

Thus

Part c) find the percentage of scores that are not significant​ (or less than 2 standard deviations away from the​ mean).

That is find: