[statistiek] hulp bij oplossen nodig
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[statistiek] hulp bij oplossen nodig
Hallo ik kom niet op het antwoord van opgave b in de volgende vraagstelling. moet ik dan liniair gaan programmeren? maar ik denk dat het op een andere manier aangepakt moet worden.
The number of cola-bottles that are produced in one hour according
to production process 1 has approximately a normal distribution with mean 600 and
standard 2. In a new production process, say 2, this number has a approximately a normal distribution mean 650 and standard deveiation 10.
a) The first 12 hours of a day the company produces according to process 1. The next
12 hours one produces according to process 2. The numbers in different periods of
one hour are independent. What is the mean and variance of the number of bottles
produced in one day of 24 hours ?
b) The variance found in a) is too large. One wants to choose a combination of the
two processes such that the variance of the number of bottles produced in one day
is less than 480. The mean value should be as large as possible. How many hours
should one produce according to process 1 and how many according to process 2 ?
c) Let X be the number of produced bottles in one day, when the combination of a) is
used (12 hours for process 1 and 12 hours for process 2). Compute the probability
that the average production per hour (X/24) is larger than 626.
Alle opmerkingen zijn welkom! bedankt alvast
The number of cola-bottles that are produced in one hour according
to production process 1 has approximately a normal distribution with mean 600 and
standard 2. In a new production process, say 2, this number has a approximately a normal distribution mean 650 and standard deveiation 10.
a) The first 12 hours of a day the company produces according to process 1. The next
12 hours one produces according to process 2. The numbers in different periods of
one hour are independent. What is the mean and variance of the number of bottles
produced in one day of 24 hours ?
b) The variance found in a) is too large. One wants to choose a combination of the
two processes such that the variance of the number of bottles produced in one day
is less than 480. The mean value should be as large as possible. How many hours
should one produce according to process 1 and how many according to process 2 ?
c) Let X be the number of produced bottles in one day, when the combination of a) is
used (12 hours for process 1 and 12 hours for process 2). Compute the probability
that the average production per hour (X/24) is larger than 626.
Alle opmerkingen zijn welkom! bedankt alvast
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Re: [statistiek] hulp bij oplossen nodig
Verplaatst naar huiswerk.
"Malgré moi, l'infini me tourmente." (Alfred de Musset)
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Re: [statistiek] hulp bij oplossen nodig
Heb wat lopen rekenen, maar kom niet uit. Weet je zeker dat de standaard deviaties zijn gegeven of de varianties?
Ik heb het volgende gedaan:
Ik heb het volgende gedaan:
\(\max_{n \in \mathbb{N}}\left\{ \mathbb{E}[nX_1 + (24-n)X_2]\right\} = \max_{n \in \mathbb{N}} \left\{600n + (24-n)650\right\}\)
\(\textrm{s.t. } 4n^2 + 100(24-n)^2 = 480 - \epsilon \textrm{\hspace{1cm} $\epsilon\geq0$}\)
Er bestaat niet een positieve \(\epsilon\)
, waarvoor dit een uitkomst geeft voor n. Dus of er zit in mijn redenering iets verkeerd, of in de opgave...Verborgen inhoud