|
Nabistai zal het maar weer eens oplossen zeker
| quote: |
Normal Distribution
Living with uncertainty
For this coursework I have chosen to do assignment B2
It states: Investigate the distribution of males´ and/ or females in families. You may choose, for example, to collect data on the distribution of girls in families of three children and to estimate the probability of a female birth.
To be able to collect the necessary data for the investigation, I will have to look at families with 3 children. The datum will be collected from pupils in the school I go to. I will collect the data by sending questionnaires to every pupil in the school from year seven (aged 11-12) to year thirteen (aged 17-18) asking them how many children are in there families and how many are male/female. From here the data will be sorted through and only the relevant questionnaires (the ones with three children in their families) will be taken out.
A sample size of thirty is thought to be sufficient in this data collection so to collect this number every successful questionnaire was given a number (136 in total). 136 was placed into a graphic calculator which then randomly gave out 30 numbers.
It should be noted that the larger the sample size the more reliable the results are likely to be.
Hypothesis: The probability of having a boy in a three-child family is above 75 %.
The probability of giving birth to a boy is the same as a girl, this can be proved by using genetic code which is below.
x y
Boy xy x xx xy
When these two are mixed there are 4 out comes:
Girl xx x xy xx
As the probability of a boy and girl has been proved equal a suitable probability model can be chosen. The most suitable model is the binomial probability model. It is also suitable because the probability of giving birth is independent; this means one event is not dependent on the other. In the instance of giving birth it means that if a mother has already had a boy the chances of having another one are exactly the same as if she had given birth to none.
The Binomial Model
The binomial model must be set so that the probability of having a boy is 0.5 and the probability of having a girl is set at 0.5. The number of times that the event must happen is 3.
The binomial model below is an example of how the final model will look it is possible from this to see how the mathematics are carried and set out.
N how many times the event happens
R Outcomes from the events
P The probability of the outcome
Using the results that will be obtained from the binomial model it will be possible to calculate the amount of families out of the 30 collected that should have 3 boys, 3 girls, 1 boy 2 girls or 2 boys 3 girls.
The 4 binomial models are below:
1 (no boys)
2 (one boy)
3 (two boys)
4 (three boys)
Results to Questionnaires
Number selected Amount of children in family Amount of boys Amount of girls
1 3 2 1
2 3 2 1
3 3 1 2
4 3 1 2
5 3 1 2
6 3 2 1
7 3 1 2
8 3 2 1
9 3 2 1
10 3 2 1
11 3 1 2
12 3 1 2
13 3 2 1
14 3 2 1
15 3 3 0
16 3 1 2
17 3 0 3
18 3 2 1
19 3 1 2
20 3 3 0
21 3 3 0
22 3 1 2
23 3 2 1
24 3 2 1
25 3 1 2
26 3 0 3
27 3 1 2
28 3 3 0
29 3 2 1
30 3 0 3
Total families questioned Amount of children in family Total male(Possible 90) Total female(Possible 90)
30 30 47 43
What the results show
From the data collected it is possible to see that out of the 30 families questioned, four families had three boys, and three families had three girls, 12 families had two boys and one girl and eleven families had two girls and one boy
Below is a probability table showing how the children in the families were distributed
Number of boys 0 1 2 3
Probability p(X) 0.1 0.366 0.4 0.133
When this is compared to the binomial probability table the results are very similar.
Binomial probability table
Number of boys 0 1 2 3
Probability p(X) 0.125 0.375 0.375 0.125
Comparing the real lie results to the binomials model shows a very strong correlation. This seems to prove that the odds of giving birth to a boy is the same as a girl, the results also prove that giving to a boy is independent of any births the mother may have had before.
Looking at both sets of results it is possible to calculate the probability of having one or more boys in a family of three children. To work out the probability of having on or more boys in a family the probabilities of having one, two or three boys in a family must be added together. Below is the working for the real life and binomial probabilities.
Real world 0.366 + 0.4 + 0.133 = 0.899
Binomial 0.375 + 0.375 + 0.125 = 0.875
Therefore it is possible to conclude that the real world model and the binomial show a strong correlation and therefore proving the original hypothesis. They prove that there is not only a higher than 75% chance of having a boy in three but that there is actually a chance of almost 90%
|
Vala, ik heb snel eventjes mijn hypothese over dit onderwerp neegepent 
___________________
"I hated going to weddings. All the grandmas would poke me saying "You're next". They stopped that when I started doing it to them at funerals."
| quote: | | Het doel van een heel deel hier is niet over muziek te praten maar door zijn deelname aan discussies een zo groot mogelijk intellect proberen aan de dag te leggen en daarmee een rare vorm van zelfbevrediging in werking stellen. 'It's a strange world' |
|
)
), verwoord als een domme kloot, maar de geste was er hé <(*^_^*)
