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435-hwk3-sub

# 435-hwk3-sub - (a What proportion of the STOR 435 students...

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STOR 435 Supplementary Problem Set 1 (1) let X N ( μ, σ 2 ), P ( X 0) = 1 / 3 and P ( X < 1) = 2 / 3. Find P ( X > 2). (2) Let X N (1 , 4), A = { 0 . 4 < X 2 . 4 } and B = { 1 . 2 X < 7 } . Find P ( A B ), P ( A B ), P ( A | B ) and P ( B | A ). (3) Let X N (1 , 4) and g ( t ) = P ( X > t ), -∞ < t < . (a) Find the value t that minimizes g ( t + 4) - g ( t ) and justify your answer. (b) Redo (a) for X N (1 , σ 2 ). Does your answer depend on σ ? Explain why. (4) Assume the distribution of STOR 435 scores follows N (75 , 81), and a score “ 60” means “pass” (with full score 100).
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Unformatted text preview: (a) What proportion of the STOR 435 students will pass? (b) In a random sample of 80 STOR 435 students, what is the probability that at least 75 students will pass? (c) If a score “ < β ” means “fail”, determine the value of β such that the failure rate for STOR 435 students is less than 3%. 1...
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