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Answer :
The minimum score required for admission to the university is 3.6.
To find the minimum score required for admission to the university, we need to determine the GRE score that corresponds to the 40th percentile of the distribution.
First, we need to find the z-score that corresponds to the 40th percentile. We can use a standard normal distribution table or a calculator to find this value.
Using a standard normal distribution table, we can look up the z-score that corresponds to a cumulative area of 0.40, which is approximately 0.25.
The z-score corresponding to a cumulative area of 0.25 is -0.25.
Next, we can use the formula for transforming a z-score to a raw score:
z = (x - mu) / sigma
where:
z is the z-score (-0.25 in this case)
x is the raw score we want to find
mu is the mean of the distribution (3.8 in this case)
sigma is the standard deviation of the distribution (0.8 in this case)
Solving for x, we get:
[tex]x = z\times sigma + \mu[/tex]
[tex]x = (-0.25)\times 0.8 + 3.8[/tex]
x = 3.6.
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Rewritten by : Barada
To determine the minimum GRE Analytical Writing score for the top 40% of students, one must find the 60th percentile of the normal distribution using a z-table, then use the formula X = mean + (z * standard deviation) with a mean of 3.8 and a standard deviation of 0.8.
To find the minimum GRE Analytical Writing score required for admission to a university that admits students in the top 40%, we need to determine the score that corresponds to the 60th percentile of the normal distribution (since 100% - 40% = 60%). In a normal distribution, percentiles can be found using a z-table or a statistical calculator which tells us the z-score associated with a given percentile.
First, we calculate the z-score for the 60th percentile. Then we use the mean and standard deviation of the distribution to find the actual score. The formula to convert a z-score to an X value (actual score) is:
X = μ + (z * σ)
Where μ is the mean, σ is the standard deviation, and z is the z-score. By plugging in the mean of 3.8 and the standard deviation of 0.8, we can find the minimum score required for admission to be in the top 40%.
Note: You will need a z-table or statistical software to find the exact z-score for the 60th percentile. This process is called inverse transformation in statistics.
