X follows normal distribution(400,64).Find the inter-quartile range of the distribution.
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asked by Raj
today at 2:24am
There are 16 pieces of data in each quartile. The inter-quartile range is
Q3 - Q1
How to find Q3-Q1?And is n=sd/4?
To find Q3 you need to look up .75 on your z-score table. You will see that the number associated with that is .674 so that means that to be in the 75th percentile (Q3) you must be 0.674 standard deviations above the mean value.
The mean is 400 so... 400 + (.674x64) = 443.13
while
Q1 would be 0.674 standard deviations below the mean (since the normal distribution is symetrical)
Q1 = 400- (.674 x 64) = 356.87
Now you need Q3 - Q1 : )
The answer is 10.784.So different from your calculations.
Hmmm... let me check some numbers...
There was another part of the question too which I did myself finding the limits within which the central 95% of the distribution lies.
LOL! (mean,sigma^2)
so the standard deviation is 8 thus
with 0.674 above and below...
gives my answer to be 10 even...
To find the inter-quartile range (IQR) of a normal distribution, you need to determine the values of the first quartile (Q1) and the third quartile (Q3).
To find Q1 and Q3, you can use the standard deviation (sd) and mean (µ) of the normal distribution. Here's how you can calculate them:
1. Find Q1:
- Calculate the z-score for Q1 using the formula:
z = (Q1 - µ) / sd
- Since Q1 corresponds to the 25th percentile, the z-score associated with it is -0.6745.
- Rearrange the formula to solve for Q1:
Q1 = (-0.6745 * sd) + µ
2. Find Q3:
- Calculate the z-score for Q3 using the formula:
z = (Q3 - µ) / sd
- Since Q3 corresponds to the 75th percentile, the z-score associated with it is 0.6745.
- Rearrange the formula to solve for Q3:
Q3 = (0.6745 * sd) + µ
3. Calculate the inter-quartile range (IQR):
- IQR is the difference between Q3 and Q1.
IQR = Q3 - Q1
In this case, you mentioned that X follows a normal distribution with mean 400 and standard deviation 64. By substituting these values into the formulas above, you can find Q1 and Q3, and then calculate the IQR.