Ch 09.pdf - Maths B Yr 12 Ch 09 Page 283 Thursday 11:53 AM...

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9 syllabus ref efer erence ence Applied statistical analysis In this cha chapter pter 9A Discrete random variables 9B Expected value of discrete random distributions 9C The binomial distribution 9D Problems involving the binomial distribution for multiple probabilities 9E Expected value, variance and standard deviation of the binomial distribution Probability distributions
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284 M a t h s Q u e s t M a t h s B Ye a r 1 2 f o r Q u e e n s l a n d Introduction Gary’s test — did he pass? Gary is sitting an aptitude test for a career in the armed forces. The test con- sists of 20 multiple-choice questions, each question with 4 alternative answers. To be accepted, Gary must answer at least 16 questions correctly. Gary is confident that he has answered 13 questions correctly but is unsure of the other 7, so he has a guess at each of these answers. What is the prob- ability that Gary is accepted into the armed forces? This situation, and others like it, will be examined further in this chapter Your Maths Quest CD-ROM contains theory, worked examples and ques- tions on Probability revision. Discrete random variables A random variable is one whose value cannot be predicted but is determined by the outcome of an experiment. For example, two dice are rolled simultaneously a number of times. The sum of the numbers appearing uppermost is recorded. The possible outcomes we could expect are {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. Since the possible outcomes may vary each time the dice are rolled, the sum of the numbers appearing uppermost is a random variable. Random variables are expressed as capital letters, usually from the end of the alphabet (for example, X , Y , Z ) and the value they can take on is represented by lower- case letters (for example, x , y , z respectively). The above situation with dice illustrates an example of a discrete random variable since the possible outcomes were able to be counted. Discrete random variables generally deal with number or size. A random variable which can take on any value is defined as a continuous random variable . Continuous random variables generally deal with quantities which can be measured, such as mass, height or time. extension e xtension Probability revision Which of the following represent discrete random variables? a the number of goals scored at a football match b the height of students in a Maths B class c shoe sizes d the number of girls in a five-child family e the time taken to run a distance of 10 kilometres in minutes THINK WRITE Determine whether the variable can be counted or needs to be measured. a Goals can be counted. a Discrete. b Height must be measured. b Continuous. c The number of shoe sizes can be counted. c Discrete. d The number of girls can be counted. d Discrete. e Time must be measured. e Continuous.
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