Homework #$5-$ Chapter$3(20$pts for turned in on time$)$

$9.(9$ points$)$ There are two major tests of readiness for college: ACT and SAT. ACT scores are reported from $1$ to $36.$ If the ACT score for all the freshman students in one college is approximately normally distributed, with mean $=21\mathrm{.}5$ and $=5\mathrm{.}4.$

$(1)(3$ points$)$The college dean decided to waive the tuition for the top $3\%$ students. In order to quality for tuition waive, how high does a student need to score on the ACT test?

$(2)(3$ points$)$The students with low ACT scores tends to struggle in college. The college wants to help those students succeed, so they provide special advising for those students. Since the resource is limited$,$ they will need to identify the bottom $5\%$ of the students with low ACT scores. How low will a student's ACT score be so that they can receive the special advising from the college?

$(3)(3$points$)$ One college professor is proposing that any student with ACT score lower than $14$ will need to take a remedial course to help preparing for the lower division college course. By the professor's proposal, what percent of the students will have to take a remedial course?

$7$