Question

You are to roll a fair die n = 102 times, each time observing if the topside of the die shows a 6 (success) or not (failure). After observing the n = 102 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 = 102 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 p? ? with a mean ?_p? = and a standard deviation ?_p? = (c) What is the probability that the proportion/percentage of your n = 102 tosses that show a six will be somewhere between 14% and 22%? Enter your answer using all the decimals you can. (d) After the n = 102 tosses of the die, you observe X = 23, the value of the sample proportion is then p? = 23/102 = 0.2255. What is the probability of observing a sample proportion that is at least this much should you decide to roll this die again 102 times? Enter your answer using all the decimals you can.

          You are to roll a fair die n = 102 times, each time observing if the topside of the die shows a 6 (success) or not (failure). After observing the n = 102 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 = 102 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 p? ? with a mean ?_p? = and a standard deviation ?_p? =

(c) What is the probability that the proportion/percentage of your n = 102 tosses that show a six will be somewhere between 14% and 22%? Enter your answer using all the decimals you can.

(d) After the n = 102 tosses of the die, you observe X = 23, the value of the sample proportion is then p? = 23/102 = 0.2255. What is the probability of observing a sample proportion that is at least this much should you decide to roll this die again 102 times? Enter your answer using all the decimals you can.

You are to roll a fair die n = 102 times, each time observing if the topside of the die shows a 6 (success) or not (failure). After observing the n = 102 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 = 102 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 p? ? with a mean ?p? = and a standard deviation ?p? =

(c) What is the probability that the proportion/percentage of your n = 102 tosses that show a six will be somewhere between 14% and 22%? Enter your answer using all the decimals you can.

(d) After the n = 102 tosses of the die, you observe X = 23, the value of the sample proportion is then p? = 23/102 = 0.2255. What is the probability of observing a sample proportion that is at least this much should you decide to roll this die again 102 times? Enter your answer using all the decimals you can.

Added by Juan Luis W.

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