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
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-> 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
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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):
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.
