Chapter8

# Chapter8 - = =-Chapter 8 The Binomial and Geometric...

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------- =====-Chapter 8 The Binomial and Geometric Distributions I ACTIVITY 8 A Gaggle of Girls The Ferrells have 3 children: Jennifer, Jessica, and Jaclyn. If we assume that a couple is equally likely to have a girl or a boy, then how unusual is it for a fam- ily like the Ferrells to have 3 children who are all girls? We have encountered problems like this in an earlier chapter. But this time we're going to use the method of simulation. If success = girl, and failure = boy, then p(success) = 0.5. We will define the random variable X as the number of girls. Then we want to simulate families with 3 children. Our goal is to determine the long- term relative frequency of a family with 3 girls, that is, P(X = 3). 1. Using a random number table, let even digits represent. "girl" and odd digits represent "boy." Select a row, and beginning at that row, read off num- bers 3 digits at a time. Each 3 digits will constitute one trial. Use tally marks in a table like this one to record the results: Do at least 40 trials. Then combine your results with those of other stu- dents in the class to obtain at least 200 trials. Calculate the relative fre- quency of the event (3 girls). 2. For variety, do the same thing as before, but this time using the calculator. Using the codes 1 = girl and 0 = boy, enter the command randInt ( O,1,3 ) . This command instructs the calculator to randomly pick a whole number from the set (0, 1) and to do this 3 times. The outcome (0, 0, l), using our codes, means {boy, boy, girl), in that order. Continue to press -Nand count until you have 40 trials. Use a tally mark to record each time you observe a (1, 1, 1) result. Calculate the relative frequency for the event (3 girls). 3. Extra for programming experts: Write a calculator program to carry out the process described above. Allow the user to specify the number of trials, and have the calculator report the relative frequency of (3 girls) as a decimal number. 1 4. Determine the total number of outcomes for this experiment. List the 1 outcomes in the sample space. Then complete the probability distribut' table for the random variable X = number of girls. Do the results of your simulations come close to the theoretical value for P(X = 3)?
-* 8.1 The Binomial ~istri~~~439-~~~ INTRODUCTION In practice, we frequently encounter experimental situations where there are two outcomes of interest. Some examples are: We use a coin toss to see which of the two football teams gets the choice of kicking off or receiving to begin the game. A basketball player shoots a free throw; the outcomes of interest are {she makes the shot; she misses). A young couple prepares for their first child; the possible outcomes are {boy; girl). A quality control inspector selects a widget coming off the assembly line; he is interested in whether or not the widget meets production requirements.

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## This note was uploaded on 12/09/2011 for the course STAT 101 taught by Professor O during the Fall '08 term at Lake Land.

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Chapter8 - = =-Chapter 8 The Binomial and Geometric...

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