Probability and Statistics: True/False Statements and Explanations

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1Probability and Statistics: True/False Statements and ExplanationsAssignments2 solutions: Due by MidnightSundayJune16th, 2013(drop box of week2)(Chapters 4, 5, and 6)Total 125 points.True/False (2points each)Chapter41. If events A and Bare independentand A is not an impossible event, then P(A/B) isnot equalto zero.TRUEIn fact P(A/B) equalsP(A)if A and B are independent,which is not zero unlessAis an impossible event.2. If events A and B are mutually exclusive, thenP(A/B) is equal to zero.TRUEThis is obviousfrom the definition of mutually exclusive events. If B occurs then A cannot occur at the sametime. Therefore P(A/B) = 0.3. The union of events A and B is given by all basic outcomes common to both A and BFALSEChapter 54. If the probability of success is 0.4 and the number of trials in a binomial distribution is 150,then its standard deviation is 36.FALSEσ=√(np(1-p)) =√(150*0.4*0.6) = 65. If a fair coin is tossed 100 times, then the variance of therandom variable defined as thenumber of heads is exactly five.FALSEσ2= np(1-p)= 100*0.5*0.5= 25. So the standard devis 5 not the Variance.6. If a fair coin is tossed 20 times then the probability of exactly 10 Tails is more than 18percent.FALSEIt is 17.62 percent7.The probability that a person catches a cold during the cold and flu season is 0.4. If 10 peopleare chosen at random, the standard deviation for the number of persons catching cold is 1.55.(Hint: convert the problem to a binomial distribution problem).TRUEHere p = 0.4 and n=10.Therefore, standard deviation = sq root of 10*0.4*0.6Chapter 68.The number of defective pencils in a lot of 1000 is an example of a continuous randomvariable.FALSEIt is aresult of counting-so discrete.9.For a continuous distribution, P(X≤100) = P(X<100).TRUESee my Instructions on this.10.All continuous random variables are normally distributed.

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