Question 970787: In 3-4, for a normal standard distribution, determine what percent of the data values are in each given range.
3. Between 1 standard deviation below the mean and 1 standard deviation above the mean
4. Berween 1 standard deviation below the mean and 2 standard deviation above the mean
This question has been bothering me so much, I need help thank you so much
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! For a normal distribution, z-score is on the left of the table, and the four figures in the table are probabilities.
1 SD below =0.1586 probability from the left end to z=-1 (50% probability from left end to z=0)
1 SD above=0.1586 from right.
That sum is 0.3172
Subtract from 1, and what is left is between -1 and 1 is 0.6828
68% of the probability is between -1 and +1 SD
From -1 to +2
0.1584 to the left is excluded as before.
Go to the z-table, and under 2.0 you see 0.4772, depending on the z-table (might be 0.9772) The 0.4772 is z above 50%; the 0.9772 is the total probability from the left side to z=+2
+2 has 0.4772 probability (from 50%).
Another way to do it is to take the 0.9772 (z=2; 2 SDs) and subtract 0.1586, which is to the LEFT of z=-1 (that is not what you want). In between is what you want, and the probability is the difference of the two numbers, 0.8186.
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