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Although economies around the world (and especially in developed nations) are nowroaringbacktolife,manychildrenarestilloutofschoolorlearningremotely.Evenoncethesechildrenreturn,thelossofeducationmayleadtolong-termeffectsonoutcomes.

Manyarealsoworriedthatthesenegativeconsequenceswillbedisproportionatelybornebydisadvantaged students,widening existingdisparities ineducation.

In order to understand the extent to which COVID-19 has widened inequality ineducation,yougatherthefollowinginformationonstudentsfromUSelementaryschoolsinMarch 2021:

25%ofallstudentsarestilllearningremotely.

Studentsareclassifiedbyparentalincomepercentileinto"High"(Top25%),Low(Bottom25%), and "Middle"(25^thto 75^thPercentile)

20%ofin-personstudentsarelow-income

20%ofmiddle-incomestudentsarelearningremotely.

Basedontheinformationabove:

a.[3 points] What percent of all students are middle-income students who arelearningremotely?

b.[5points]Whatpercentofhigh-incomestudentsarelearningremotely?

You are also interested in the effect of remote learning on academic achievement.Tostudy this, you gather a sample containing the test scores of students from Spring 2021.Assumethat,intruth,25%ofstudentsarelearningremotelyinthefullUSpopulation.

c.[5 points] Initially you gather data on just 5 students from Rhode Island.You areworried, however, that none of them will be learning remotely in a sample thissmall.What is the probability that at least one of the students in your sample of 5studentsis learning remotely?

Convinced that you need a larger sample, you gather information on 1,200 students fromRhodeIsland.

d.[3 points] In this new sample of 1,200 students, what is the expectation (orexpected value) of the number of students in yoursamplewho are learningremotely?

e.[6 points] In this new sample of 1,200 students, what is the chance that thefraction of students in your sample who are learning remotely is smaller than27.5%?