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 probability of observing a sample proportion that is at least this much should you decide to roll this die again 120 times? Enter your answer using all the decimals
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 probability of observing a sample proportion that is at least this much should you decide to roll this die again 120 times? Enter your answer using all the decimals
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text: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 probability of observing a sample proportion that is at least this much should you decide to roll this die again 120 times? Enter your answer using all the decimals
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