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Answer :
Answer:
24.25
Step-by-step explanation:
The minimum admission score is at the 70th percentile of the normal distribution which, according to a z-score table, corresponds to a z-score of 0.524.
The z-score, for any given value X, is determined by:
[tex]z=\frac{X-\mu}{\sigma}[/tex]
If the mean score is 21 and the standard distribution is 6.2, the minimum required score for admission is:
[tex]0.524=\frac{X-21}{6.2}\\X=24.25[/tex]
The minimum score required for admission is 24.25.
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Final answer:
The minimum score required for admission to a university that accepts the top 30% of ACT Reading scores involves finding the z-score for the 70th percentile and then using the mean and standard deviation of the scores to calculate the minimum ACT score.
Explanation:
To find the minimum score required for admission for a university that admits students whose scores are in the top 30% of the ACT Reading scores, we need to calculate the corresponding z-score for the 70th percentile (because the top 30% would start at the 70th percentile and go higher). Using the given mean (μ = 21) and standard deviation (σ = 6.2), we can find this z-score from a standard normal distribution table or by using a calculator that has a function for inverse normal probabilities.
Once we have the z-score for the 70th percentile, we can use the z-score formula to solve for the corresponding ACT score (x):
Z = (x - μ) / σ
After obtaining the z-score:
- x = (Z*σ) + μ
We plug in the values of the z-score, μ, and σ to find the minimum ACT Reading score required for admission.
