Probability and Statistics: True/False Statements and Explanations

Evaluates key statistical concepts through true/false statements and explanations.

Amelia Ward
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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(X100) = P(X<100).TRUESee my Instructions on this.10.All continuous random variables are normally distributed.

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2FALSEContinuous random variables can be highly skewed andnon-normal.Even if it issymmetrical it may not be normal but other distribution like t-distribution.A normal randomvariable is a popular example of a continuous random variable, but a continuous r.v. need not benormal.11.The mean of a standard normal distribution is always equal to 1.FALSE.Its mean is zeroand variance (or std deviation) equal to 1.12. Ifthe sample size isas large as1000, wecan safelyuse the normal approximation tobinomial even for small p.FALSE(Instructions on Ch6): For example if p is .001 then npwould be only 1 even if sample size is 1000.Multiple Choice(3points each)Chapter 41. Two mutually exclusive events havingpositive probabilities are ______________ dependent.A.NeverB.SometimesC.AlwaysThey are necessarily dependent because the occurrence of one (seriously) affects the probabilityof the other (makes it zero). Instructions on Ch 4 page 42.If P(A)>0 and P(B)>0 and events A and B are independent, then:A.P(A)=P(B)B.P((A|B))=P(A)C.P(AB)=0D.P(AB)=P(A)/P(B/A)E. Both A and C are correctSee My Instructions on Ch 4 page 5. Independence does not imply equality ofprobabilities. Sothe first choice is clearly wrong. The third choice applies to mutually exclusive events notindependent events. The fourth choice is also incorrect because there should be multiplication onthe right hand side not division. So thecorrect answer is B.3. A recent marketing survey tried to relate a consumer’s awareness of a new marketingcampaign with their rating of the product. Consumers rated their awareness as low, medium andhigh, and rated the product as poor, fair, or good. The results are presented below:RatingAwarenessLowMediumHighPoor0.100.150.07

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3Fair0.060.110.06Good0.070.110.27What is the probability that a consumer who ranked the product as fair had a high awareness ofthe adcampaign?A.0.06B.0.26C.0.23D.0.15E.0.40The completed table is:RatingAwarenessLowMediumHightotalPoor0.100.150.070.32Fair0.060.110.060.23Good0.070.110.270.45Total0.230.370.401.00P(HighAwareness/Fair) = 0.06/0.23 = 0.26 rounded to two decimal places.4. With the data in question 3 above, what is the probability that a randomly selected consumereither has a low awareness or rated the product poor?A. 0.23B. 0.32C. 0.55D.0.45E.0.10The completed table is:RatingAwarenessLowMediumHightotalPoor0.100.150.070.32Fair0.060.110.060.23Good0.070.110.270.45Total0.230.370.401.00
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