Please solve this ASAP the answer doesn't have to be pretty

Question 5: [1+2+3+1+1 =8 ] a) What is the pdf and write the conditions that need to be satisfied to be a pdf? b) SAT scores are distributed nearly normally with mean 1500 and standard deviation 300. ACT scores are distributed nearly normally with mean 21 and standard deviation 5. 1. A university admissions officer wants to determine which of the two applicants scored better on their standardized test with respect to the other test takers: Sam. who earned an 1800 on her SAT. or Jim. who scored a 24 on his ACT? i1. Find the IQR of SAT score. 111. Calculate the probability of a randomly selected applicant scored 15 to 25 m his ACT. iv. Calculate the probability of a randomly selected applicant scored more than 1750 m his SAT