SOLUTION: A typical adult has an average IQ score of 105 with a standard deviation of 20. If 20 randomly selected adults are given an IQ test, what is the probability that the sample mean sc

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Question 975205: A typical adult has an average IQ score of 105 with a standard deviation of 20. If 20 randomly selected adults are given an IQ test, what is the probability that the sample mean scores will be between 85 and 125 points
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Find the standard error.
SE=sigma%2Fsqrt%28n%29
SE=20%2Fsqrt%2820%29
SE=sqrt%2820%29
So then the margin of error equals,
ME=z%5Bc%5D%2ASE
ME=z%5Bc%5D%2Asqrt%2820%29
But you know the ME is equal to,
ME=125-105=20
20=z%5Bc%5D%2Asqrt%2820%29
z%5Bc%5D=sqrt%2820%29
Find the probability corresponding to a two tailed area between -sqrt%2820%29 and sqrt%2820%29.
P%28-sqrt%2820%29%29=3.87x10%5E%28-6%29
So then the area of interest is the area when you subtract twice this value from 1.
P=0.99999
Almost 100%.