Question 647522
A psychologist studied self-esteem scores and found the sample data set to be normally distributed with a mean of 50 and a standard deviation of 5. 
Part A**What raw score cuts off the bottom 10.03% of this distribution? 
Steps: 
What is the z-score that cuts off the bottom 10.03% of this distribution?
z = invNorm(0.1003) = -1.280 
What is the raw score that cuts off the bottom 10.03% of this distribution? 
x = zs + u
x = -1.280*5 + 50 = 43.6
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Part B**What percentage of the scores is between 57.5 and 65? 
Steps: 
What is the z-score that corresponds to the raw score of 57.5?
z(57.5) = (57.5-50)/5 = 1.5
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What is the z-score that corresponds to the raw score of 65?
z(65) = (65-50)/5 = 3
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What percentage of the scores is between 57.5 and 65? 
P(57.5<= x <=65) = P(1.5<= z <=3) = 0.0655 = 6.55%
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Part C:**A raw score of 35 is associated with what percentile? 
Steps: 
What is the z-score associated with a raw score of 35?
z(35) = (35-50)/5 = -15/5 = -3
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A raw score of 35 is associated with what percentile?
P(z < -3) = normalcdf(-100,-3) = 0.0013 = 0.13%
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Part D:**What raw scores mark the middle 34% of this distribution?
Steps: 
What are the z-scores that mark the middle 34% of this distribution? 
The z-score below the mean is
z = invNorm(.50-0.17) = -0.44
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The z-score above the mean is +0.44
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What is the raw score below the mean?
x = -0.44*5+50 = 47.8
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Cheers,
Stan H.
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