You are to roll a fair die n = 112 times, each time observing the number of dots appearing on the topside of the die. The number ofdots showing on the topside of toss i is a random variable represented by Xi, i = 1, 2, 112....,(a) Consider the distribution of the random variable ✗¿. Find the mean and the standard deviation of the number of dots showing onthe uppermost face of a single roll of this die.μ.Χ. 18.8333 Enter your answer using all the decimals you can.=σχί4.0848 Enter your answer using all the decimals you can.(b) Now think about the average of your n = 112 tosses of the fair die. What can you say about the distribution of this average?Complete the sentence, Enter your answer using all the decimals you can.The distribution of X is approximately Normal with a mean μx=0.1667 and a standard deviation σx=(c) What is the probability that the average topside on your n = 112 tosses will be somewhere between 3.3 and 3.7? Enter youranswer using all the decimals you can.0.7413(d) What is the probability that the average of your n = 112 tosses is greater than 4.05? Enter your answer using all the decimals youcan.0.0202

Let Xi denote the result of a single roll of a fair die.…

Answered: You are to roll a fair die n = 112…

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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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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An HP laser printer is advertised to print text documents at a speed of 18 ppm (pages per minute). The manufacturer tells you that the printing speed is actually a Normal random variable with a mean of 17.55 ppm and a standard deviation of 3 ppm. Suppose that you draw a random sample of 12 printers. Part i) Using the information about the distribution of the printing speeds given by the manufacturer, find the probability that the mean printing speed of the sample is greater than 18.15 ppm. (Please carry answers to at least six decimal places in intermediate steps. Give your final answer to the nearest three decimal places). Probability (as a proportion) ...
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