SOLUTION: A package delivery service divides their packages into weight classes. Suppose that packages in the 14 to 20 pound class are uniformly distributed, meaning that all weights within

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Question 1187691: A package delivery service divides their packages into weight classes. Suppose that packages in the 14 to 20 pound class are uniformly distributed, meaning that all weights within that class are equally likely to occur.
In the light of the above case, you are required to answer the following questions:
1. Find the probability that package weighs between 15 and 16.5 pounds.
2. Find the probability that a package weighs less than 15 pounds.
3. Find the probability that a package weighs at least 18 pounds.
4. Calculate the variance and the standard deviation of the distribution.
Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
The mean is 17 pounds (a+b)/2
between 15-16.5 pounds is 1.5 pounds, and the total range is 6 pounds. Probability is 0.25
fewer than 15 pounds is probability 1/6 (from 14-15 only).
at least 18 pounds is probability 1/3 or 2/6 (from 18-20 pounds.
sd is sqrt((b-a)^2/12)
that is sqrt(36/12) or sqrt (3), or 1.732 pounds
variance is sd ^2 or 3 pounds^2