Problem 4. (1 point) 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 of dots showing on the topside of toss i is a random variable rep- resented by Xi, i = 1, 2, ..., 112. (a) Consider the distribution of the random variable Xi. Find the mean and the standard deviation of the number of dots showing on the uppermost face of a single roll of this die. μχ. σχ = Enter your answer using all the decimals you can. 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 ⚫is exactly Normal ⚫is skewed to the right ⚫ is Uniform has an unknown shape with a mean μx= 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 your answer using all the decimals you can. (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 you can.

Problem 4. (1 point) 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 of dots showing on the topside of toss i is a random variable rep- resented by Xi, i = 1, 2, ..., 112. (a) Consider the distribution of the random variable Xi. Find the mean and the standard deviation of the number of dots showing on the uppermost face of a single roll of this die. μχ. σχ = Enter your answer using all the decimals you can. 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 ⚫is exactly Normal ⚫is skewed to the right ⚫ is Uniform has an unknown shape with a mean μx= 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 your answer using all the decimals you can. (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 you can.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.2: Expected Value And Variance Of Continuous Random Variables

Problem 10E

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