a) Consider the 689599.7 rule. 68% of the observations in a N distribution are w
ID: 3128072 • Letter: A
Question
a) Consider the 689599.7 rule. 68% of the observations in a N distribution are within ± 1. Where does the “1” come from? If the central proportion in the distribution is 0.68, then the remaining area is 1.000.68=0.32. That area of 0.32 is split evenly in the two tails, so each tail has an area of 0.16. Find the z score for the area in the left tail and the z score for the area in the right tail. Are those z scores close to ± 1? b) 95% of the observations in a N distribution are within ± 2. Where does the “2” come from? Use the same approach as above to find the z score for the area in the left tail and the z score for the area in the right tail. Are those z scores close to ± 2? c) 99.7% of the observations in a N distribution are within ± 3. Where does the “3” come from? Use the same approach as above to find the z score for the area in the left tail and the z score for the area in the right tail. Are those z scores close to ± 3?
Explanation / Answer
a)
Yes.
Using a table, the z score corresponding to a left tailed area of 0.16 is
z = -0.99 which is close to -1.
The same way, the z score corresponding to a right tailed area of 0.16 (or left tailed area of 0.84) is
z = 0.99 which is close to 1.
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b)
Yes.
Using a table, the z score corresponding to a left tailed area of 0.025 is
z = -1.96 which is close to -2.
The same way, the z score corresponding to a right tailed area of 0.025 (or left tailed area of 0.975) is
z = 1.96 which is close to 2.
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c)
Yes.
Using a table, the z score corresponding to a left tailed area of 0.0015 is
z = -2.97 which is close to -3.
The same way, the z score corresponding to a right tailed area of 0.0015 (or left tailed area of 0.9985) is
z = 2.97 which is close to 3.
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