// Numbas version: finer_feedback_settings
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Na\u030ar man skal ta førerprøven ma\u030a man ta en teoriprøve der mange elever trenger flere forsøk for a\u030a besta\u030a. Trafikkskolen Lappen har funnet ut at antall forsøk elevene benytter for a\u030a besta\u030a prøven er som vist i sannsynlighetstabellen nedenfor. Den diskrete variabelen \ud835\udc4b representerer antall forsøk for a\u030a besta\u030a teoriprøven.
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![](\"resources/question-resources/Skjermbilde_2022-02-27_kl._14.54.55.png\")
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PS: alle sannsynligheter gis som et tall mellom 0 og 1, ikke i prosent. Bruk punktum som komma i besvarelsene.
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Hva er sannsynligheten for at en tilfeldig elev bruker mer enn to forsøk for a\u030a besta\u030a eksamen?
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Hva er sannsynligheten for at en tilfeldig elev bruker færre enn to forsøk for a\u030a besta\u030a eksamen?
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Regn ut forventede antall forsøk pa\u030a eksamen for en student X. Det vil si: finn \ud835\udd3c(\ud835\udc4b)
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Regn ut variansen Var (\ud835\udc4b).
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Avgiften til Statens vegvesen er 490 kroner for hver gang man ga\u030ar opp til prøven. La variabelen \ud835\udc4c være hvor mye en elev bruker pa\u030a teoriprøven for a\u030a besta. Beregn forventningen \ud835\udd3c(\ud835\udc4c).
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![](\"resources/question-resources/Skjermbilde_2022-02-27_kl._15.12.29.png\")
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\ud835\udc38(\ud835\udc4b)=
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\ud835\udc38(\ud835\udc4c)=
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Cov(X,Y) =
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Na\u030ar man selger en bolig, kan man tegne en eierskifteforsikring. Hos en megler velger 60 prosent av selgerne a\u030a tegne eierskifteforsikring. Megleren fa\u030ar 5 nye kunder.
Merk: sannsynlighetene oppgis som et tall mellom 0 og 1 og kommatall skrives med punktum.
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Hva er sannsynligheten for at akkurat 4 av kundene tegner eierskifteforsikring?
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\ud835\udc43(\ud835\udc4b = 4)=
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Hva er sannsynligheten for at minst en av kundene tegner eierskifteforsikring?
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\ud835\udc43(\ud835\udc4b ≥ 1)=
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Et flyselskap selger reiser innenlands og utenlands og tilbyr forsikring til kundene na\u030ar de kjøper reisen. Av 100 reiser som ble solgt var 40 utenlandsreiser. Det var totalt 80 av kundene som valgte a\u030a tegne forsikring. Anta at sannsynligheten for at en kunde tegner forsikring er uavhengig av hva slags reise vedkommende kjøper. Hva er sannsynligheten for at 30 av utenlandskundene tegnet forsikring?
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En aksje har en dagskurskurs pa\u030a gjennomsnittlig 100 kroner. Populasjonsstandardavviket til aksjekursen er 2 kroner og aksjekursen er normalfordelt.
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Hva er sannsynligheten for at kursen en tilfeldig dag er under 103 kroner?
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Hva er sannsynligheten for at kursen en tilfeldig dag er over 95 kroner?
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Hva er sannsynligheten for at kursen en tilfeldig dag er mellom 88 og 102 kroner?
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![](\"resources/question-resources/Skjermbilde_2022-02-27_kl._16.04.21.png\")
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En kunde ringer etter en drosje. Finn sannsynligheten for at ventetiden blir mer enn 15 minutter.
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10 kunder bestiller en drosje. De bestiller pa\u030a ulike tidspunkt, slik at vi kan anta at ventetiden deres er uavhengig av hverandre.
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Hva er sannsynligheten for at alle 10 kundene ma\u030a vente i mer enn 15 minutter?
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Hva er sannsynligheten for at de 10 kundene i gjennomsnitt ma\u030a vente mer enn 15 minutter?
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Et meningsma\u030alingsinstitutt spør 100 tilfeldig utvalgte personer av befolkningen i en kommune om de er for eller mot a\u030a beholde statskirken. 58 av personene svarer at de er for a\u030a beholde ordningen.
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Lag et punktestimat for populasjonsandelen som er for a\u030a beholde statskirken.
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Lag et 95% tosidig konfidensintervall for populasjonsandelen som er for a\u030a beholde statskirken.
Merk: i denne oppgaven er svaret du skal skrive feilmarginen til kofidensintervallet: ![](\"resources/question-resources/Skjermbilde_2022-02-27_kl._16.11.29.png\")
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Et utvalg pa\u030a 60 tilfeldig valgte studenter i Norge svarer i en undersøkelse av de i gjennomsnitt bruker 2.33 timer pa\u030a matlaging i uken, med et standardavvik pa\u030a 0.6. Lag et tosidig 95% konfidensintervall for gjennomsnittlig tid brukt pa\u030a matlaging for norske studenter.
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Merk: i denne oppgaven er svaret du skal skrive feilmarginen til kofidensintervallet, siden du har fått punktestimatet for utvalget(2.33)
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Et utvalg pa\u030a 16 tilfeldig valgte studenter i Norge svarer i en undersøkelse av de i gjennomsnitt bruker 2.33 timer pa\u030a matlaging i uken, med et standardavvik pa\u030a 0.6. Lag et tosidig 95% konfidensintervall for gjennomsnittlig tid brukt pa\u030a matlaging for norske studenter.
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Merk: i denne oppgaven er svaret du skal skrive feilmarginen til kofidensintervallet, siden du har fått punktestimatet for utvalget(2.33)
\n![](\"resources/question-resources/Skjermbilde_2022-02-27_kl._16.11.29_p1t1dlD.png\")
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Merk - 1: oppgavene er de samme oppgavene som i utdelt oppgavesett.
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Merk - 2: alle kommatall skrives med punktum, ikke komma. Med andre ord: 3.41 er et gyldig kommatall, men 3,41 er ikke det.
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Merk - 3: beregningene tar utgangspunkt i to desimalers nøyaktighet og vanlige avrundingsregler.
Merk - 4: alle sansynligheter besvares som et tall mellom 0 og 1, ikke i prosent
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