A Pew Research Center report published on February 2, 2022 says, “In a national survey by Pew Research Center, 54% of U.S. adults say they have a favorable opinion of the Supreme Court while 44% have an unfavorable view, and 84% say justices should not bring their political views into decisions.” Answer the given problems based on the assumption that the above figures represent the true proportion of current U.S. people’s opinion. 4.1. If 20 U.S. adults are selected at random, what is the probability that less than half the selected people have favorable view on U.S. Supreme Court? 4.2. If 20 U.S. adults are selected at random, what is the probability that more than half the selected people have unfavorable view on U.S. Supreme Court? 4.3. If 5,128 U.S. adults were interviewed, what are the expected value of the number of people that answered that the justices should not bring their political views into decisions? What is the probability standard deviation in this case?
A Pew Research Center report published on February 2, 2022 says, “In a national survey by Pew Research Center, 54% of U.S. adults say they have a favorable opinion of the Supreme Court while 44% have an unfavorable view, and 84% say justices should not bring their political views into decisions.” Answer the given problems based on the assumption that the above figures represent the true proportion of current U.S. people’s opinion.
4.1. If 20 U.S. adults are selected at random, what is the probability that less than half the selected people have favorable view on U.S. Supreme Court?
4.2. If 20 U.S. adults are selected at random, what is the probability that more than half the selected people have unfavorable view on U.S. Supreme Court? 4.3. If 5,128 U.S. adults were interviewed, what are the expected value of the number of people that answered that the justices should not bring their political views into decisions? What is the probability standard deviation in this case?
If each trial has only two possible outcomes, that is, success and failure, the probabilities of success or failure for each trial remains the same and trials are independent then the number of success or failure can be assumed to follow binomial distribution.
For a binomially distributed random variable , the probability of getting number of success in trials, can be given as, , where be the success probability for each trial.
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