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[solution]: An express mail service charges a special rate for any package


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An express mail service charges a special rate for any package that weighs less than 1 lb. Let x denote the weight of a randomly selected parcel that qualifies for this special rate. The probability distribution of x is specified by the density curve shown below. Use the fact that area of a trapezoid = (base)(average of two side lengths)to answer each of the following questions:

(a) What is the probability that a randomly selected package of this type weighs at most 0.4lb? between 0.35 and 0.5 lb? at least 0.85lb?

P(x?0.4) =

P(0.35?x?0.5) =

P(x?0.85) =


(b) It can be shown that?x= 7/12 and?2x= 11/144. What is the probability that the value ofxis more than 1 standard deviation from the mean value? (Round the answer to four decimal places.)

P(xis more than one standard deviation from the mean value) =


 


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