SOLUTION: For a normal distribution curve with a mean of 7 and a standard deviation of 5, which of the following ranges of the variable will define an area under the curve corresponding to a

Question 1085500: For a normal distribution curve with a mean of 7 and a standard deviation of 5, which of the following ranges of the variable will define an area under the curve corresponding to a probability of approximately 34%?
Found 2 solutions by Boreal, Theo:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
That is +/-z=0.955
z=(x-mean)/sd
z*sd=4.775 or 4.8
range will be 7+/-4.8
(2.2, 11.8)
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the mean is 7 and the standard deviation is 5.

if you want a probability of 34% to be between certain limits of the normal distribution curve, then you will have 100% - 34% = 66% outside of these limits.

cut that in half and you will have 33% outside the left limit and 33% outside the right limit

33% outside the right limit is to the right of that limit.

this means that 67% is to the left of that limit.

you want to find the z-score for that right limit.

look in the z-score table for a percentage of 67% to the left of the z-score.

that would be a ratio of .67 that you're looking for.

you can also use a calculator, which is a lot easier.

we'll use the table for now to see what we get.

the table shows a ratio of .67 is associated with a z-score of .44

.44 has 33% of the area under the distribution curve to the right of it.

since the distribution table is symmetric, then -.44 has 33% of the area under the distribution curve to the left of it.

so limits are a z-score of -.44 to .44

your mean is 7 and your standard deviation is 5

you want to relate your z-score to your raw score.

the formula to use is z = (x-m) / s

z is the z-score
x is the raw score
m is the raw score mean
s is the standard deviation.

in your problem, the formula becomes

-.44 = (x-7) / 5 and .44 = (x-7) / 5

solve for x in each of these and you will get:

x = 5 * -.44 + 7 and x = 5 * .44 + 7

your raw score limits will be between 4.8 and 9.2

with these limits, 34% of the area under the normal distribution curve will be between them.

visually, this looks like this:

it looks like it's a little off because the area shows as .3401.

that's due to rounding.

i used a calculator and got the following limits.

4.800434151 to 9.199565849

visually that looks like this:

you can see that the area between shows as .34 which is a lot closer.

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