7.27 An express mail service charges a special rate for any package that weighs less than 1 pound. 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 following density curve:

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 0.5 pound? between 0.25 and 0.5 pound? at least 0.75 pound?

b. It can be shown that mx 5 712 and s2x5 11144. What is the probability that the value of x is more than 1 standard deviation from the mean value?

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Density Density = 0.5+x 1.5 1.0 0.5 0