Scores on the verbal Graduate Record Exam (GRE) are normally distributed with a mean of 600 and a standard deviation of 120. Suppose a graduate school requires that students score at or above the 80th percentile. Approximately what score is required on this exam?
Scores on the verbal Graduate Record Exam (GRE) are normally distributed with a mean of 600 and a standard deviation of 120. Suppose a graduate school requires that students score at or above the 80th percentile. Approximately what score is required on this exam?
Scores on the verbal Graduate Record Exam (GRE) are normally distributed with a mean of 600 and a standard deviation of 120. Suppose a graduate school requires that students score at or above the 80th percentile. Approximately what score is required on this exam?
Scores on the verbal Graduate Record Exam (GRE) are normally distributed with a mean of 600 and a standard deviation of 120. Suppose a graduate school requires that students score at or above the 80th percentile. Approximately what score is required on this exam?
b.Practice using the 68-95-99.7 Rule by completing the normal distribution below with horizontal scale and percentages in each interval. [Use the graph in (c) and (d).]
Transcribed Image Text:**Understanding GRE Scores: Normal Distribution Curve**
In this diagram, we visualize the distribution of GRE scores using a normal distribution curve. This curve helps to understand the extent to which the scores of the test-takers are distributed around the mean score.
1. **Bell Curve Representation**:
The diagram shown is a bell-shaped curve, indicating a normal distribution where the scores progressively increase to a peak (mean) and symmetrically decrease.
2. **Percentages within Standard Deviations**:
The curve is divided into different sections representing standard deviations from the mean, marking the percentage of scores within each section.
- **68%**: The central part of the curve, shaded green and bounded by two dashed blue lines, indicates that 68% of the test-takers' scores fall within one standard deviation of the mean. This means that 68% of the students scored in this central range, showing the concentration around the average score.
- **95%**: Expanding outward, the next section still in green but bounded by additional dashed blue lines, represents 95% of the scores falling within two standard deviations from the mean. This includes the initial 68% and extends to a wider range of scores.
- **99.7%**: The widest section, encompassing almost the entire bell curve, signifies that 99.7% of the scores lie within three standard deviations from the mean. This indicates the near-total distribution of scores within this extended range.
3. **Horizontal and Vertical Axes**:
- **Horizontal Axis**: It typically represents the range of GRE scores.
- **Vertical Axis**: It indicates the frequency or the number of students achieving those scores, peaking at the mean and decreasing symmetrically towards the ends.
4. **Implications**:
Understanding these percentages and their corresponding sections helps in assessing how relatively high or low a particular score is, compared to the general test-taker population.
Use this visualization to reinforce your understanding of score distribution and how most scores cluster around the mean, with fewer scores at the extreme high and low ends.
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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