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.
---
Find the z-score with a right tail of 12%: invNorm(0.88) = 1.1758
score = 1.1758*4.7+21.5 = 27.0224
=======================================

b. If 1300 students are randomly selected, how many would be expected to have a test score that would meet the college’s requirement?
---
0.12*1300 = 156
=======================

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
=====================================
Cheers,
Stan H.