(1 point) You are to roll a fair die n120 times, each time observing if the tops

Question

(1 point) You are to roll a fair die n120 times, each time observing if the topside of the die shows a 8 (success) ar not (failure). After observing the n topside showed a 6. This count is represented by the random variable X 120 tosses, you are to count the number of tines the (a) The distribution of X ? 4 with a mean l and a standard deviation Ii. Use at least two decimals. 120 tosses that show a six. What can you say about the distribution of this proportion? Complete the sentence, using at least four decimals in each numeric (b) Now think about the proportion of your n answer. The distribution of p2 with a mean p- and a standard deviation op- (c) What is the probability that the proportion/percentage of your n-120 tosses that show a six will be somewhere between 14% and 22%? Use at least four decimals in your answer. d After the n 20 tosses of the die you observe X = 27, the value of the sample proportion s then p = should you decide to roll this die again 120 times? Use at least four decimals in your answer = 0 225 what is the probability of observing a sample propo ton hat is at least this much

Explanation / Answer

a) The distribution of X is BINOMIAL with mean 20 and standard deviation 4.08248.
b) The distribution of p^ is NORMAL with mean 0.1667 and standard deviation 0.0340.

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