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 and a standard deviation of 4.7. Find the lowest test score that a student could get and still meet the colleges requirement.
Please help me out. Thanks!
Your questionwas edited so that there is one question per guidelines. The same general method applies to each of your questions:
We are given a mean `mu=21` ,and a standard deviation `sigma=4.7` .
We are asked to find the lowest score that is in the top 12% of all scores.
First we find the z-score such that 12% are above it -- this corresponds to a z-score with 88% below it. From a standard normal table we find that a z-score of 1.17 has 87.9% below it, while a z-score of 1.18 has 88.1% below it. Thus we could use either 1.17,1.18, or split the difference to get 1.1754. (My calculator gives z=1.174986791 so I will use z=1.175)
Now we want to find the x that corresponds to a z of 1.175. To compute z we use: `z=(x-mu)/sigma` . Multiplying both sides by `sigma` and adding `mu` we get `x=zsigma+mu`
The cut score will be `x=1.175(4.7)+21=26.52`
Thus the lowest composite score will be 27.