4- (15 Points) A sample of 200 students at a certain university was taken after

Question

4- (15 Points) A sample of 200 students at a certain university was taken after the midterm ex One hundred students reported staying up all midterm anud night before the midtermandthe other 'me ' ndredst dents did not those who stayed nd of those who did not stay up all night befone the whdncem 60 did wwell on as to sbwey did well or poorly on the misdhers mideerm. aterm30) did wo a) Prepare a contingency table for this data b) What is the probability that a randomly selected student do not stay up all niglt before a miduerm exam? c) What is the probability that a randomly selected student ilities,xplaelected student do not May up all night hefore a midkerm or docs poorly on the midhcrm ilitics, explain d) What's the a randomly selected student who stays up all night before a midterm does well on the midhcrm probability that a r probability that ando mly the probabilither staying hes, explain whether staying up all night before a midierm is independent of doing poorly on

Explanation / Answer

a)

b) probability=100/200 =0.5

c) probability=30/100 =0.3

d)probability=60/200 =0.30

e)probability=(100+70)/200 =0.85

f)here probability of staying up=100/200=0.5

probability of doing good =90/200=0.45

probability of doing good and staying up =30/200=0.15

as P( doing good and staying up) is not equal to P(doing good) *P(staying up)

therefore they are not independent,

did well not did well total stayed up 30 70 100 not stayed up 60 40 100 total 90 110 200

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