Probability and Statistical Analysis in Different Contexts, Exams of Statistics

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2 Section 1 Exam

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ion for reducing symptoms associatedwith a I trials of Clarinex-D, 5% of the patients expe- [ect. An SRS of 20 Clarinex-D usersis chosen rho experiencedinsomnia is recorded. y that exactly 3 erperiencedinsomnia as a side fr\

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2. According^ to Arnerican^ Airlines, Flight 2I5 from Oriando to Los Angeles is on time 90%on time 90% of the time. Suppose of the time. Supposethat 150that 150 such such fliehts durins the past 20 flights during the past 20 years are randomly seiected. (a) What is the distribution that the number of on-time flights in the above samplefollows approximately? Is this approxirnation good enough? Explain.

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' , \T 3. As reported by the U.S. National Center for Health Statistics,^ the mean serum high density lipoprotein (FIDL) cholesterolof males 20 to 29 years old is p, -- 47.^ Dr.^ Oswiecrniskirarrdomly^ selected15 of his male patients within that age group and found the mean HDL cholesterollevel to be r^ - 48.3. Supposethat the sample^ comesfrom a population which is normally distributed with standard deviation o -^ I2.5. Construct a 98% confidence interval for the mean HDL chelesterolfor all Dr.^ Osu'iecmiski's20- to 29-

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year-old male patients.

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"4. To improve fuel efficiencyand reduce pollution, the owner of a trucking

fleet decidesto install a new fuel catal;'st in all his semitrucks. He feelsthat the catalyst rvill heip to increasethe number of miles per galion. Before the installation, his semitruckshad a mean gas mileageof 5.9 miles per gallon. An SRS of t2 sernitrucksafter the installation shows a mean gas mileage of n :^ 6.31. Supposethat the gas mileageis normall;r distributed with a standard deviation a -^ 0.5. Is the sampleresult good evidencethat the new fuel catalyst works? State the hypotheses,calculate a test statistic and its P-value, and give your conclusion at significance level a -^ 0.05.

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m According to Yatroo!Finance,the averagedaily ],'olumeof ,fotorola^ stock in 2000was p -^ 11.4million sharcs.rvith standard deviatiorro :- 8.3 million. Based on an SRS of 35 trading days in 2004,the mean number of Motorola stock sharestraded daily turrred out to be 13.3 million. Is the averagedaily volume of Motorola stock significantly different rn 2004 as compared with 2000? Supposethat the daily volume is normall;' distributed with the same o -^ 8.3 miliion unchangedfor },Iotorolastock. State the hypotheses,calcu- late a test statistic and its P-value, and give your conclusionat significance l e v e le : 0. 0 5 "

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6. According to the U.S. Bureau of Labor Statistics,there are the following probabilities about a randomly selectedernployedindividual: (_ I me i,nd,iui,dualhas more tltan one job I the indiu'idual t th" ,ind,iu,id,,uat (^) has more than one job

a randomly selectedemployedindividual is

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individual is

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(a) What is the probability that male and a rnultiple-job holder?

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a randomly selectedem the individual is male?{ --I" (^) i r- Fr . l.- \r\f 11 )\

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