Your friend’s professor gives out reasonably hard exams 70% of the time, and ridicu- lously hard...

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Your friend’s professor gives out reasonably hard exams 70% ofthe time, and ridicu- lously hard exams 30% of the time. On hardexams, each student’s score on the exam is a normally distributedrandom variable with ?H = 70 and ?H = 10. On ridiculously hardexams, each student’s score on the exam is a normally distributedrandom variable with ?R = 50 and ?R = 15. Suppose you have fourfriends in the class, not just one. Let A be the average score ofyour four friends: A= (F1 +F2 +F3 +F4)/ 4 Where F1 is your firstfriend’s score, and F2 is your second friend’s score. Find E[A] andV ar(A) if the exam is ridiculously hard. (e) Find E[A] and V ar(A)if the exam is reasonably hard. (f) Since A is the sum of normalrandom variables, it is itself a normal random variable. Find P (A> 65) if the exam is reasonably hard, and if it is ridiculouslyhard. (g) If A is greater than 65, what is the probability the examwas ridiculously hard?

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dEA and V arA if the exam is ridiculously hardOn ridiculously hard exams each students score on the exam isa normally distributed random variable with 50 and 15Let A be the average score of your four friends A F1 F2 F3F4 4F1F2F3F4 follow normal distribution withmean 50 and standard deviation 15A F1 F2 F3 F4 4EA EF1 EF2 EF3EF4 4 VarA VarF1VarF2VarF3VarF4 42 EA 50VarA eEA and V arA if the See Answer

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