SOLUTION: The weight of a .5 cubic yard bag of landscape mulch in uniformly distributed over the interval from 38.5 to 41.5 pounds. a. Give a mathematical expression for the probability den

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Question 849152: The weight of a .5 cubic yard bag of landscape mulch in uniformly distributed over the interval from 38.5 to 41.5 pounds.
a. Give a mathematical expression for the probability density function.
b. What is the probability that a bag will weigh more than 40 pounds?
c. What is the probability that a bag will weigh less than 39 pounds?
d. What is the probability that a bag will weigh between 39 and 40 pounds?
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
The weight of a .5 cubic yard bag of landscape mulch in uniformly distributed over the interval from 38.5 to 41.5 pounds.
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a. Give a mathematical expression for the probability density function.
mean = (38.5+41.5)/2 = 80/2 = 40
std = ?
6sigma = 41.5-38.5 = 3
sigma = 1/2
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b. What is the probability that a bag will weigh more than 40 pounds?
P(wt. > 40) = P(z > 0) = 0.5
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c. What is the probability that a bag will weigh less than 39 pounds?
z(39) = (39-40)/(1/2) = -2
P(wt < 39) = P(z < -2) = binomcdf(-100,-2) = 0.0228
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d. What is the probability that a bag will weigh between 39 and 40 pounds?
Ans: 0.5-0.0228 = 0.4772
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Cheers,
Stan H.
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