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Questions and Answers
What percent of applicants scored above 450 on the GRE, given a mean of 544 and a standard deviation of 103?
What percent of applicants scored above 450 on the GRE, given a mean of 544 and a standard deviation of 103?
82%
What is the percentile of a 33.40 millimeter diameter camshaft in a normally distributed population where 70% are greater?
What is the percentile of a 33.40 millimeter diameter camshaft in a normally distributed population where 70% are greater?
30th percentile
What are the x-values for Q1, Q2, and Q3 in a normal distribution with a mean of 480 and standard deviation of 32?
What are the x-values for Q1, Q2, and Q3 in a normal distribution with a mean of 480 and standard deviation of 32?
458, 480, 502
What is the probability that a randomly selected person's z-score from a normal population would be above z=-1.8?
What is the probability that a randomly selected person's z-score from a normal population would be above z=-1.8?
What is the GRE score at the upper quartile, Q3, for applicants with a mean of 544 and standard deviation of 103?
What is the GRE score at the upper quartile, Q3, for applicants with a mean of 544 and standard deviation of 103?
What is the z-score for the lowest quartile of any normal curve?
What is the z-score for the lowest quartile of any normal curve?
What percent of applicants had a GRE score below 625, given a mean of 544 and a standard deviation of 103?
What percent of applicants had a GRE score below 625, given a mean of 544 and a standard deviation of 103?
What percent of applicants scored between 500 and 700 on the GRE with a mean of 544 and standard deviation of 103?
What percent of applicants scored between 500 and 700 on the GRE with a mean of 544 and standard deviation of 103?
What is the GRE score at the 77th percentile with a mean of 544 and standard deviation of 103?
What is the GRE score at the 77th percentile with a mean of 544 and standard deviation of 103?
What is the normal curve area, to the nearest whole percent, between z=-0.38 and z=+1.5?
What is the normal curve area, to the nearest whole percent, between z=-0.38 and z=+1.5?
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Study Notes
GRE Scores in Psychology Applicants
- GRE scores are normally distributed with a mean (m) of 544 and a standard deviation (s) of 103.
- Score above 450: 82% of applicants scored above this GRE score.
- Score below 625: 78% of applicants had a score below this threshold.
- Score between 500 and 700: 60% of applicants scored within this range.
- Upper quartile (Q3) score: The GRE score at Q3 is 613.
- 77th percentile GRE score: Calculated to be 620.
Camshaft Diameter Distribution
- In a population of camshaft diameters, 70% exceed 33.40 millimeters.
- A diameter of 33.40 millimeters is identified as the 30th percentile.
Quartiles in Normal Distribution
- For a normal distribution with a mean of 480 and a standard deviation of 32:
- First quartile (Q1) x-value: 458.
- Second quartile (Q2 or median): 480.
- Third quartile (Q3) x-value: 502.
- The z-score for the lowest quartile (Q1) is -0.67.
Probability and Z-Scores
- If randomly selecting an individual from a normal population, the probability of obtaining a z-score above -1.8 is 96%.
- The normal curve area between z=-0.38 and z=+1.5 is 58%.
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