Question 1191930: For a normal distribution if the value of mean is 70 and standard deviation is 15.75 find two points.
(a) in which it contains 98% area between them
,(b) in which it contains 95% area between them
((c) in which it contains 85% area between them
,(d) In which it contains 60% area between them
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! mean is 70 and standard deviation is 15.75.
you want to find two points that contain different percentages of the area under the normal distribution curve between them.
you would be looking for the critical z-scores that would have the stated area between them.
a statistical calculator makes this easy.
one online calculator that you can use can be found at https://davidmlane.com/hyperstat/z_table.html
here are your results using this calculator.
to solve this problem, you select value from an area, enter the area (decimal equivalent, not percent), enter the mean and the standard deviation, select between and then calculate.
if you want z-scores rather than raw scores, enter 0 for mean and 1 for standard deviation.
if you do that, then you will have to use the z-score formula to find the raw score.
there is no need, however, because the calculator does that for you.
i did one just to show you what i mean.
you do everything you did above except you enter 0 for the mean and 1 for the standard deviation.
you enter .98 for the area and select between.
it tells you that the z-scores are -2.326 to 2.326
to find the raw score, you use the z-score formula.
for z-score of -2.326, the formula becomes -2.326 = (x - 70) / 15.75
solve for x to get:
x = -2.326 * 15.75 + 70 = 33.3655.
this is very close to what you got working from raw scores directly, but it will not always be right on because of rounding differences.
let me know if you have any questions.
theo
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