High School

Suppose ACT Science scores are normally distributed with a mean of 21.2 and a standard deviation of 4.7. A university plans to admit students whose scores are in the top 35%. What is the minimum score required for admission? Round your answer to the nearest tenth, if necessary.

Answer :

The minimum score required for admission is 22.90.

Here we have to find the minimum score required for admission.

Z-score:

Z-score measures how much standard deviation the measure is from the mean.

The formula for z-score:

Z = X- μ/ б

mean(μ) = 21.2

standard deviation (б) = 4.7

University plans to admit students whose scores are in the top 35%.

Top 35%, so at least 100- 35 = 65th percentile. The 65th percentile is the value of X when Z has a p-value of 6.5. So it is X when Z = 0.385

So putting the value:

0.385 = X - 21.2 / 4.7

X = 22.9095

So the minimum score is 22.90.

To know more about the z-score refer to the link given below:

https://brainly.com/question/25638875

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