The scores on the GRE are normally distributed with a mean of 541 and a standard deviation of 89. Use the 68-95-99.7 rule to find the percentage of people taking the test who score between 363 and 541

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Scores on the GRE​ (Graduate Record​ Examination) are normally distributed with a mean of 549 and a standard deviation of 138. Use the 68 dash 95 dash 99.7 Rule to find the percentage of people taking the test who score below 273.

To find the percentage of people taking the test who score between 363 and 541 on the GRE, we can use the 68-95-99.7 rule, also known as the empirical rule or the three-sigma rule. This rule states that in a normal distribution:

- Approximately 68% of the data falls within one standard deviation of the mean.
- Approximately 95% of the data falls within two standard deviations of the mean.
- Approximately 99.7% of the data falls within three standard deviations of the mean.

In this case, we are given that the mean (μ) is 541 and the standard deviation (σ) is 89.

First, let's calculate the Z-scores for the given scores using the formula: Z = (X - μ) / σ, where X is the given score.

Z-score for X = 363:
Z = (363 - 541) / 89
Z = -178 / 89
Z = -2

Z-score for X = 541:
Z = (541 - 541) / 89
Z = 0 / 89
Z = 0

Now, we can use the Z-scores to determine the percentage of people scoring between 363 and 541.

Since the Z-score for X = 541 is 0, this means that 50% of the population falls below this score.

To find the percentage of people scoring between 363 and 541, we need to find the area under the normal distribution curve between the Z-scores of -2 and 0.

Looking up these Z-scores in a standard normal distribution table, we find that the area to the left of Z = -2 is approximately 0.0228, and the area to the left of Z = 0 is 0.5.

To find the area between these two Z-scores, we subtract the smaller area from the larger area:
0.5 - 0.0228 = 0.4772

Therefore, approximately 47.72% of people taking the GRE score between 363 and 541.

for a mean of 541, with a sd of 89

we would have:
541-89 <---> 541+89 (one standard deviation)
452 <---> 630 ---------68%

452-89 <---> 630+89 (two standard deviations)
363 <---> 719 -------- 95%
since 541 is the mean
363<---> 541 would be 1/2 of 95% or 47.5%