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(1 point) You are to roll a fair die n 105 times, each time observing if the top

ID: 3314626 • Letter: #

Question

(1 point) You are to roll a fair die n 105 times, each time observing if the topside of the die shows a 6 (success) or not (failure). After observing the n = 105 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 is Binomial 4. with a mean 17.50 E and a standard deviation 3.82 iii. Use at least two decimals. (b) Now think about the proportion of your n 105 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 answer. The distribution of p ? $ with a mean = | and a standard deviation (c) What is the probability that the proportion/percentage of your n-105 tosses that show a six will be somewhere between 14% and 22%? Use at least four decimals in your answer. (d) After the n = 105 tosses of the die, you observe X = 24, the value of the sample proportion is then p-24-02286. What is the probability of observing a sample proportion that is at least this much should you decide to roll this die again 105 times? Use at least four decimals in your answer. 105

Explanation / Answer

b) Dist of proportion is normal with mean = 17.5 and SD = 3.82

c) 0.14 * 105 = 14.7

0.22 * 105 = 23.1

SD = 3.82

z1 = (14.7 - 17.5)/3.82 = - 0.73

z2 = (23.1 - 17.5)/3.82 = 1.47

P = 0.6965

d) X = 24

z1 = (24 - 17.5)/3.82 = 1.7

P = 0.0446