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

Covers key statistical concepts including probability and distribution.

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Statistics and Probability Assignment: Binomial Distributions, Normal Distributions,Confidence Intervals, and Expected Value CalculationsLane5.A fair coin is flipped 9 times. What is the probability of getting exactly 6 heads?This is abinomial distribution where N=9 p=1/2 x=6P(x=6)=9C6*.56*.53= .164111.A group of students at a school takes a history test. The distribution is normalwith a mean of 25, and a standard deviation of 4. (a) Everyone who scores inthe top 30% of the distribution gets a certificate. What is the lowest scoresomeone can get and still earn a certificate?Let x= lowest scoresomeone can get and still earn a certificatez-score corresponding toprobability of .7 = Norm.S.Inv(.7)=.5244 =(x-25)4x= 25 +.5244*4= 27.09=27(b) The top 5% of the scores get tocompete in a statewide history contest. What is the lowest score someone canget and still go onto compete with the rest of the state?z.95=1.645=(x-25)/4x= 25+1.645*4= 31.58=3212. A personclaims to be able to predict the outcome of flipping a coin. Thisperson is correct 16/25 times. Compute the 95% confidence interval on theproportion of times this person can predict coin flips correctly. Whatconclusion can you draw about this test of his ability to predict the future?The 95% confidence interval on theproportion of times this person can predict coin flips correctly: p±Margin of errorp=16/25 =.64; q=1-.64=.36

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