Approximately 400,000 students took the GRE in 2009. Observed mean for the Verbal score was 540 with a standard deviation of 80, and the observed mean quantitative score was 500 with a standard deviation of 100.
Assuming distribution was normal, answer the following:
How many students scores are below the mean?
How many students scores are above the mean?
How many students scores fall between one standard deviation below and above the mean?
How many students scores are higher than two standard deviations above the mean?
I am so confused!! I've watched countless videos and read, and re-read the power points...I can't wrap my brain around this...please help!!
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No problem, I'm here to help explain!
To answer these questions, we can use the concept of the normal distribution. In a normal distribution, the mean is located at the center, and the standard deviation gives us information about the spread or variability of the data.
1. How many students' scores are below the mean?
To answer this, we need to find the area under the curve to the left of the mean. Since the distribution is symmetric, we know that 50% of the students' scores are below the mean. Therefore, approximately 50% of the 400,000 students, which is 200,000 students, have scores below the mean.
2. How many students' scores are above the mean?
Similar to the previous question, 50% of the students' scores are above the mean since the distribution is symmetric. Thus, approximately 200,000 students' scores are above the mean.
3. How many students' scores fall between one standard deviation below and above the mean?
To find the answer, we need to look at the area between one standard deviation below and one standard deviation above the mean. In a normal distribution, about 68% of the data falls within one standard deviation of the mean. Therefore, approximately 68% of 400,000, which is 272,000 students, have scores between one standard deviation below and one standard deviation above the mean.
4. How many students' scores are higher than two standard deviations above the mean?
To answer this, we need to calculate the area under the curve to the right of two standard deviations above the mean. In a normal distribution, approximately 2.5% of the data falls above two standard deviations above the mean. So, around 2.5% of the 400,000 students, which is approximately 10,000 students, would have scores higher than two standard deviations above the mean.
I hope this explanation helps clarify how to answer these questions. Let me know if there's anything else I can assist you with!