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  • Level: GCSE
  • Subject: Maths
  • Word count: 6897

Obtain information to make a report on family size and the structure of families of particular size (number of boys/girls).

Extracts from this document...

Introduction

14th April 2001. Probability Models For Data. Coursework Title Obtain information to make a report on family size and the structure of families of particular size (number of boys/girls). To carry out this investigation I carried out a survey of 450 families. The survey was taken in my school by randomly selecting 450 individuals and asking them how many children their parents have. I did included half brothers/sisters, but decided not to include step brothers/sisters as I felt this may produce some anomalies to my investigation and also these people are not genetically related. I have found two separate statistics for the probability of male and female births in the Probability Models For Data textbook. One states that they are both equally likely and therefore there is a 0.5 chance of each birth being either male or female. The other statistic I found in the textbook stated that the probability of a male birth was more likely than a female birth, it states that the probability of a male birth is 0.513 and the probability of a female birth 0.487. These probabilities were calculated from a census taken in 1991. Once I had completed the survey I organised the data into tables of increasing family size. The data can de seen on the following pages. I decided that I would analyse the number of male births. I chose to analyse the data using the binomial model. I chose this model for the following reasons > Outcomes are independent of each other, they are said to be mutually exclusive. > A random variable, X is associated with the number of male births. The first thing I did was work out the probability of a male birth in each of the separate family sizes. To do this I totalled up the number of boys in the family size and then divided this figure by the total number of children in the family size. ...read more.

Middle

Using Probabilities From The Census. Family Of One Number of families = 49 Probability of male birth = 0.513 Probability of female birth = 0.487 P(X=0) = 1 (0.513)0 (0.487)1 = 0.487 0 P(X=1) = 1 (0.513)1 (0.487)0 = 0.513 1 Expected frequencies are: 0.487 x 49 = 23.863 0.513 x 49 = 25.137 Family Of Two Number of families = 141 Probability of male birth = 0.513 Probability of female birth = 0.487 P(X=0) = 2 (0.513)0 (0.487)� = 0.237 0 P(X=1) = 2 (0.513)� (0.487)� = 0.4997 1 P(X=2) = 2 (0.513)� (0.487)0 = 0.263 Expected frequencies are: 0.237 x 141 = 33.44 0.4997 x 141 = 70.45 0.263 x 141 = 37.1 Family Of Three Number of families = 150 Probability of male birth = 0.513 Probability of female birth = 0.487 P(X=0) = 3 (0.513)0 (0.487)� = 0.116 0 P(X=1) = 3 (0.513)� (0.487)� = 0.365 1 P(X=2) = 3 (0.513)� (0.487)� = 0.384 2 P(X=3) = 3 (0.513)� (0.487)0 = 0.1350 3 Expected frequencies are: 0.116 x 150 = 17.325 0.365 x 150 = 54.75 0.384 x 150 = 57.67 0.135 x 150 = 20.25 Family Of Four Number of families = 86 Probability of male birth = 0.513 Probability of female birth = 0.487 P(X=0) = 4 (0.513)0 (0.487)4 = 0.0562 0 P(X=1) = 4 (0513)� (0.487)� = 0.237 1 P(X=2) = 4 (0.513)� (0.487)� = 0.374 2 P(X=3) = 4 (0.513)� (0.487)� = 0.263 3 P(X=4) = 4 (0.513)4 (0.487)0 = 0.0693 Expected frequencies are: 0.0562 x 86 = 4.84 0.237 x 86 = 20.38 0.374 x 86 = 32.21 0.263 x 86 = 22.62 0.0693 x 86 = 5.9 Family Of Five Number of families = 15 Probability of male birth = 0.513 Probability of female birth = 0.487 P(X=0) = 5 (0.513)0 (0.487)5 = 0.0274 0 P(X=1) = 5 (0.513)� (0.487)4 = 0.144 1 P(X=2) ...read more.

Conclusion

0 4 4 0 4 4 0 4 4 0 4 4 0 4 4 0 4 4 0 4 4 1 3 4 1 3 4 1 3 4 1 3 4 1 3 4 1 3 4 1 3 4 1 3 4 1 3 4 1 3 4 1 3 4 1 3 4 1 3 4 1 3 4 1 3 4 1 3 4 1 3 4 1 3 4 1 3 4 1 3 4 1 3 4 1 3 4 1 3 4 1 3 4 1 3 4 1 3 4 1 3 4 1 3 4 1 3 4 2 2 4 2 2 4 2 2 4 2 2 4 2 2 4 2 2 4 2 2 4 2 2 4 2 2 4 2 2 4 2 2 4 2 2 4 2 2 4 2 2 4 2 2 4 2 2 4 2 2 4 2 2 4 2 2 4 2 2 4 2 2 4 2 2 4 2 2 4 2 2 4 2 2 4 2 2 4 2 2 4 2 2 4 2 2 4 2 2 4 2 2 4 2 2 4 3 1 4 3 1 4 3 1 4 3 1 4 3 1 4 3 1 4 3 1 4 3 1 4 3 1 4 3 1 4 4 0 4 4 0 4 4 0 4 4 0 4 4 0 4 4 0 4 4 0 Family Size Boys Girls 5 1 4 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 3 2 5 3 2 5 3 2 5 3 2 5 4 1 5 4 1 5 4 1 5 4 1 5 4 1 Family Size Boys Girls 6 1 5 6 1 5 6 2 4 6 3 3 6 3 3 6 3 3 6 3 3 6 3 3 6 5 1 ...read more.

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