c) Three coin are tossed. Write down the sample space hence copy and complete the table of probabilities distribution P(X = x) of X = 0, 1, 2, and 3 heads below hence find the expected value E(X) X p(x) 0 1318 2 3

Select all that apply. We show that our sample statistics have (at minimum) a somewhat normal distribution because this allows us to use t and z critical values. this allows us to use t and z tables for probabilities. this tells us that our sampling is appropriate. normal distributions are cool and that's all we talk about in this class.

You are to roll a fair die n = 120 times, each time observing if the topside of the die shows a 6 (success) or not (failure). After observing the n = 120 tosses, you are to count the number of times the topside showed a 6. This count is represented by the random variable X. (a) The distribution of X ? with a mean and a standard deviation Enter your answer using all the decimals you can. (b) Now think about the proportion of your n = 120 tosses that show a six. What can you say about the distribution of this proportion? Complete the sentence, Enter your answer using all the decimals you can. The distribution of ? with a mean and a standard deviation σ you can. ☐ 2 2 ☐ (c) What is the probability that the proportion/percentage of your n = 120 tosses that show a six will be somewhere between 15% and 22%? Enter your answer using all the decimals you can. (d) After the n = 120 tosses of the die, you observe X = 27, the value of the sample proportion is then = 270 = 0.225. What is the…

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