SOLUTION: A psychologist studied self-esteem scores and found the data set to be normally distributed with a mean of 50 and a standard deviation of 6. 1: What is the z-score associated wi

Question 1041056: A psychologist studied self-esteem scores and found the data set to be normally distributed with a mean of 50 and a standard deviation of 6.
1: What is the z-score associated with a raw score of 47?
2: A raw score of 47 is associated with what percentile?
3: What are the z-scores that mark the middle 95% of this distribution?
4: What is the raw score below the mean?
5: What is the raw score above the mean?
6: What is the median of this distribution?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A psychologist studied self-esteem scores and found the data set to be normally distributed with a mean of 50 and a standard deviation of 6.
1: What is the z-score associated with a raw score of 47?
z(47) = (47-50)/6 = -3/6 = -1/2
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2: A raw score of 47 is associated with what percentile?
Ans:: P(x < 47) = P(z < -0.5) = normalcdf(-100,-0.5) = 0.3085 = 30.85%
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3: What are the z-scores that mark the middle 95% of this distribution?
Find the z-values which have a right or a left tail of 2.5%
z = -1.96 and z = 1.96
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4: What is the raw score below the mean?
x = -1.96*6 + 50 = 38.24
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5: What is the raw score above the mean?
x = +1.96*6 + 50 = 61.76
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6: What is the median of this distribution?
median = 50
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Cheers,
Stan H.
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