Question 464210: A college requires applicants to have an ACT score in the top 12% of all test scores. The ACT scores are normally distributed, with a mean of 21.5 and a standard deviation of 4.7.
i) type of distribution: _sampling distributions of mean______________
ii) find the mean: __21.5 points________ and standard deviation: ____4.7 points______
iii) find the following:
a. Find the lowest test score that a student could get and still meet the college’s requirement.
b. If 1300 students are randomly selected, how many would be expected to have a test score that would meet the college’s requirement?
c. How does the answer to part (a) change if the college decided to accept the top 15% of all test scores?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A college requires applicants to have an ACT score in the top 12% of all test scores. The ACT scores are normally distributed, with a mean of 21.5 and a standard deviation of 4.7.
i) type of distribution: _sampling distributions of mean______________
ii) find the mean: __21.5 points________ and standard deviation: ____4.7 points______
iii) find the following:
a. Find the lowest test score that a student could get and still meet the college’s requirement.
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Find the z-score with a right tail of 12%: invNorm(0.88) = 1.1758
score = 1.1758*4.7+21.5 = 27.0224
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b. If 1300 students are randomly selected, how many would be expected to have a test score that would meet the college’s requirement?
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0.12*1300 = 156
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c. How does the answer to part (a) change if the college decided to accept the top 15% of all test scores?
Find the z-value with a left tail of 0.85: invNorm(0.85) = 1.0364
score = 1.0364*4.7+21.5 = 26.3712
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Cheers,
Stan H.
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