Statistics and Probability Assignment: Binomial Distributions, Normal Distributions, Confidence Intervals, and Expected Value Calculations

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Statistics and Probability Assignment: Binomial Distributions, Normal Distributions, Confidence Intervals, and Expected Value Calculations Lane 5. A fair coin is flipped 9 times. What is the probability of getting exactly 6 heads? This is a binomial distribution where N=9 p=1/2 x=6 P(x=6)= 9 C 6 *.5 6 *.5 3 = .1641 11. A group of students at a school takes a history test. The distribution is normal with a mean of 25, and a standard deviation of 4. (a) Everyone who scores in the top 30% of the distribution gets a certificate. What is the lowest score someone can get and still earn a certificate? Let x= lowest score someone can get and still earn a certificate z - score corresponding to probability of .7 = Norm.S.Inv(.7)=.5244 =(x - 25)4 x= 25 +.5244*4= 27.09=27 (b) The top 5% of the scores get to compete in a statewide history contest. What is the lowest score someone can get and still go onto compete with the rest of the state? z . 95 = 1.645 = (x - 25)/4 x= 25+1.645*4= 31.58=32 12. A person claims to be able to predict the outcome of flipping a coin. This person is correct 16/25 times. Compute the 95% confidence interval on the proportion of times this person can predict coin flips correctly. What conclusion can you draw about this test of his ability to predict the future? T he 95% confidence interval on the proportion of times this person can predict coin flips correctly : p ± Margin of error p=16/25 =.64; q=1 - .64=.36
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