Question

Suppose that a packaging service charges a specific rate for packages based on their weight. The cost is$0.20 per lb .

a. suppose that 50% of the packages are betweeon 0 and 10 lbs, 30% between 10 and 20 lbs, and 20% between 20 and 30 lbs. Within each category , the distribution of weights is uniformly distributed. what is the average cost of a package?

b. what is the probability that a package weighs more than 22 lbs conditional on knowing that it weighs more than 16 lbs.

Answer 1

The cost of packaging service is $ 0.2 per lb .The weight of packages follow Uniform Distribution .

There are three categories of weights :

• 50 % of packages belong to first category of weights between 0 and 10 lbs .

• 30 % of packages belong to second category of weights between 10 and 20 lbs .

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• 20 % of packages belong to third category of weights between 20 and 30 lbs .

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Expected Weight of the Package

  Average cost of a Package

( b ) Probability that package weighs more than 22 lbs given that it weighs more than 16 lbs .

.........Since ,

...... By Law of Total Probability

....................... Note , as it is a sure event .