SOLUTION: the distribution of IQ scores has a mean of 120 and a standard deviation of 8, use the theorem to determine the interval containing at least 8/9 of the IQ scores. At least what per

Question 1002529: the distribution of IQ scores has a mean of 120 and a standard deviation of 8, use the theorem to determine the interval containing at least 8/9 of the IQ scores. At least what percentage of these scores must lie between 104 and 136 ?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
the distribution of IQ scores has a mean of 120 and a standard deviation of 8, use the theorem to determine the interval containing at least 8/9 of the IQ scores.
----
Chebyshev says "at least 1-(1/n)^2 % of the data lies within n
standard deviations of the mean".
----
If 1-(1/n)^2 = 8/9, (1/n)^2 = (1/9) and n = 3
------
The interval:
Lower bound:: 120-3*8 = 96
Upper bound:: 120+3*8 = 144
--------------------
At least what percentage of these scores must lie between 104 and 136 ?
104 = 120-8n
8n = 16
n = 2
----
136 = 120+8n
8n = 16
n = 2
----
Ans: % of data within 2 std of the mean = 1-(1/2)^2 = 0.75 = 75%
------------
Cheers,
Stan H.
---------
RELATED QUESTIONS
IQ test scores are standardized to produce a normal distribution with a mean of u=100... (answered by ewatrrr)

IQ scores are normally distributed with a mean u=100 and a standard deviation o=15.... (answered by Nate)

IQ scores are normally distributed with a mean u=100 and a standard deviation o=15.... (answered by stanbon)

An IQ test has a mean of 100 and a standard deviation of 15. Assume a normal... (answered by Boreal)

IQ test scores are randomized to produce a normal distribution with a mean of 100 and a... (answered by stanbon)

IQ scores are normally distributed with a mean of 100 and a standard deviation of 12.... (answered by Boreal)

A psychologist wants to estimate the standard deviation of IQ scores. It is widely... (answered by VFBundy)

A psychologist wants to estimate the standard deviation of IQ scores. It is widely... (answered by Boreal)

Hello, I would appreciate it very much to get assistance with a problem: Scores of... (answered by Theo)