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Midterm

MATH 2565 Midterm: MATH 2565 Assignment 2 SolutionsExam


Department
Mathematics and Statistics
Course Code
MATH 2565
Professor
Cindy Fu Yuejiao
Study Guide
Midterm

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▼❆❚❍ ✷✺✻✺ ✲ ❋❛❧❧ ✷✵✶✾
❆ss✐❣♥♠❡♥t ✷
✭❉✉❡ ❉❛t❡✿ ❖❝t♦❜❡r ✾✱ ✷✵✶✾✮
✺✳✻✽✳
▲❡t X=t❤❡ ♥✉♠❜❡r ♦❢ ❜✉②❡rs ✇❤♦ ♣✉r❝❤❛s❡ ✇❤✐t❡ ✢✐♣ ✢♦♣s✳ XB(30,0.5)
❙♦❧✉t✐♦♥✿
❛✳ µ= (30)(0.5) = 15σ2= (30)(0.5)(0.5) = 7.5σ=7.5 = 2.7386
❜✳
P(µ2σXµ+ 2σ) = P(9.5228 X20.4772)
=P(X20) P(X9)
= 0.9786 0.0214
= 0.9572
❘ ❝♦❞❡✿
❞❜✐♥♦♠✭✷✵✱✸✵✱✵✳✺✮✰❞❜✐♥♦♠✭✶✾✱✸✵✱✵✳✺✮✰❞❜✐♥♦♠✭✶✽✱✸✵✱✵✳✺✮✰❞❜✐♥♦♠✭✶✼✱✸✵✱✵✳✺✮
✰❞❜✐♥♦♠✭✶✻✱✸✵✱✵✳✺✮✰❞❜✐♥♦♠✭✶✺✱✸✵✱✵✳✺✮✰❞❜✐♥♦♠✭✶✹✱✸✵✱✵✳✺✮✰❞❜✐♥♦♠✭✶✸✱✸✵✱✵✳✺✮
✰❞❜✐♥♦♠✭✶✷✱✸✵✱✵✳✺✮✰❞❜✐♥♦♠✭✶✶✱✸✵✱✵✳✺✮✰❞❜✐♥♦♠✭✶✵✱✸✵✱✵✳✺✮
❯s✐♥❣ ❈❤❡❜②s❤❡✈✬s ❘✉❧❡ ✇✐t❤ k= 2✱ t❤❡r❡ ✐s ❛t ❧❡❛st 0.75 ♦❢ t❤❡ ✈❛❧✉❡s ✇✐t❤✐♥ 2
st❛♥❞❛r❞ ❞❡✈✐❛t✐♦♥s ♦❢ t❤❡ ♠❡❛♥✳
❝✳ ▲❡t Fi=❣r♦✉♣ i❤❛s ❡①❛❝t❧② 15
P(Fi) = P(X= 15) = 0.1445
P(❛t ❧❡❛st ♦♥❡ ❣r♦✉♣ ❤❛s ❡①❛❝t❧② ✶✺) = 1 P(♥❡✐t❤❡r ❣r♦✉♣ ❤❛s ❡①❛❝t❧② ✶✺)
= 1 P(F
1F
2)
= 1 P(F
1)P(F
2)
= 1 (0.8555)(0.8555)
= 1 0.7319
= 0.2681
❘ ❝♦❞❡✿
✶✲✭✶✲❞❜✐♥♦♠✭✶✺✱✸✵✱✵✳✺✮✮✯✭✶✲❞❜✐♥♦♠✭✶✺✱✸✵✱✵✳✺✮✮
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