For bone density scores that are normally distributed with a mean of O and a sta

Question

For bone density scores that are normally distributed with a mean of O 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. significanty low (or at least 2 standard deviations below the mean). o. not significant (or less than 2 standard deviations away from the mean). a. The percentage of bone density scores that are significantly high ilk Round to two decimal places as needed.) b. The percentage of bone density soores that are significantly low is Round to two decimal places as needed.) The percentage of bone density scores that are not significant is0 c. Round to two decimal places as needed.)

Explanation / Answer

a) P(2 standard deviation above the mean)

= P(z > 2)

= 0.0228

So,

Percentage of bone density scores that are significantly high = 2.28%

b) By symmetry,

Percentage of bone density scores that are significantly low = 2.28%

c)

Percentage of bone density scores that are not significant = 100% - 2(2.28%) = 95.44%

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