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Problem 1: Simulating Rolling Two Four-Sided Dice (no data set) We will be comparing empirical (relative frequencies based on an observation of a real-life process) to theoretical (long-run relative frequency) probabilities.We will use StatCrunch to simulate rolling two four-sided dice.Conduct the following simulation by using the steps below: Step 1: Under Applets à Simulation à Select Dice rolling from the menu.
Build the probability distribution for the sum of two four-sided dice (i.e. list the possible values of the random variable, X (sum of two four-sided dice) and each value’s corresponding probability) in table form and present this table in your document.Use the x-axis above and rules of theoretical probability to calculate your probabilities.Present the probabilities as fractions or decimals in the table.Note, you can use this table to calculate your theoretical probabilities in parts (c) – (h).
Under Event in the applet, enter: “Sum of 2 rolls equals 7.” Use options à copy to copy this chart into your document.
Now calculate the theoretical probability that“Sum of 2 rolls equals 7” using the sample space or the probability distribution built in part (b). State this probability as a decimal rounded to three decimal places in a sentence.
Under Event now find: “Sum of 2 rolls greater than or equal to 7.” Use options à copy to copy this chart into your document.
Now calculate the theoretical probability that“Sum of 2 rolls greater than or equal to 7” using the sample space or the probability distribution built in part (b). State this probability as a decimal to rounded to three decimal places in a sentence.
Under Event find: “Sum of 2 rolls less than 7” Use options àcopy to copy your answer into your document.
Now calculate the theoretical probability that“Sum of 2 rolls less than 7” using the sample space or the probability distribution built in part (b).State this probability as a decimal rounded to three decimal places in a sentence.