GRE scores are normally distributed with a mean μ = 500 and a standard deviation of σ = 100. A sample of size n = 25 is drawn from this distribution.
What is the first quartile of the sampling distribution of the mean?
Okay so I know the first quartile is the first 25%, and I know I need to use z scores and such.
I set up my equation liiiike 0.25 = (y-500) / 20. The 20 comes from the standard deviation (100) divided by the square root of n (25). So if I solve algebraically I get 505. Is this right? Do I need the actual z score for the first quartile?
What is the first quartile of the sampling distribution of the mean?
Okay so I know the first quartile is the first 25%, and I know I need to use z scores and such.
I set up my equation liiiike 0.25 = (y-500) / 20. The 20 comes from the standard deviation (100) divided by the square root of n (25). So if I solve algebraically I get 505. Is this right? Do I need the actual z score for the first quartile?
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Standard deviation of sampling distribution = σ/√n = 100/√25 = 100/5 = 20
That's ok
Now we use z-score table to find z-score such that P(z
http://www.regentsprep.org/Regents/math/…
P(z < -0.675) = 0.25
So now we calculate z-score of y, and equate it to -0.675 (not 0.25)
This will give you a result below the mean (which you would expect for Q1, as opposed to 505 which is above the mean)
(y - 500) / 20 = -0.675
y - 500 = −13.5
y = 486.5
Ματπmφm
That's ok
Now we use z-score table to find z-score such that P(z
P(z < -0.675) = 0.25
So now we calculate z-score of y, and equate it to -0.675 (not 0.25)
This will give you a result below the mean (which you would expect for Q1, as opposed to 505 which is above the mean)
(y - 500) / 20 = -0.675
y - 500 = −13.5
y = 486.5
Ματπmφm