Please help. An eccentric (and rich) university alumnus has set up ascholarship
ID: 2915786 • Letter: P
Question
Please help.
An eccentric (and rich) university alumnus has set up ascholarship fund which pays $0, $20,000 or $50,000 to allqualifying students. Students first qualifyfor one of the scholarship amounts provided they finish theirfirst year university with at least a 3.0 gpa. The valueof the scholarship that each qualifyingstudent receives is determined by flipping two faircoins. If both are heads they are awarded the$50,000 scholarship. If exactly one of the coins inheads they are awarded the $20,000 scholarship. If bothcome up tails the student, unfortunately, receivesnothing.
a) Suppose gpa’s are normally distributed with mean 2.85and standard deviation 0.3409. Define the probabilitydistribution of the amount each studentin the general student population receives.
b) What is the expected amount any random student willreceive?
c) In a room of 100 randomly selected students that justfinished their first year, what the probability that at least30 of them received a scholarship? Hint: Use the sampling distribution of the sampleproportion to approximate the probability.
d) Given that a student received nothing, what is theprobability that their gpa was below 2.5?
e) What is the probability that 2 randomly selected studentsreceived exactly $70,000 total inscholarships?