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Answer :
The minimum score needed to be considered for admission is 29.72.
To find the minimum score needed to be considered for admission, we need to determine the score that corresponds to the top 6% of applicants.
First, we know that the average ACT score submitted to the university is 26.
Since the scores are normally distributed with a standard deviation of 2.4, we can use the Z-score formula to find the minimum score.
The Z-score formula is given by:
Z = (X - μ) / σ
where X is the score we want to find, μ is the mean, and σ is the standard deviation.
To find the Z-score corresponding to the top 6% of applicants, we need to find the Z-score that corresponds to the cumulative probability of 0.94 (1 - 0.06).
Using a standard normal distribution table or calculator, we find that the Z-score corresponding to a cumulative probability of 0.94 is approximately 1.55.
Now, we can solve for X:
1.55 = (X - 26) / 2.4
Multiply both sides by 2.4:
3.72 = X - 26
Add 26 to both sides:
X = 29.72
Therefore, the minimum score needed to be considered for admission is 29.72.
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