The weight of a .5 cubic yard bag of landscape mulch is uniformly distributed over the interval from 38.5 to 41.5 pounds. Give a mathematical expression for the probability density function. What is the probability that a bag will weigh more than 40 pou

The probability density function can be represented as f(x) = 2/(41.5-38.5) = 2/3, since the weight is uniformly distributed over the interval. The probability that a bag will weigh more than 40 pounds is the area under the probability density function from 40 to 41.5 pounds, which can be calculated as [(41.5 - 40) * 2/3] / (41.5 - 38.5) = 0.5. Therefore, the probability that a bag will weigh more than 40 pounds is 0.5 or 50%. The probability that a bag will weigh less than 39 pounds is the area under the probability density function from 38.5 to 39 pounds, which can be calculated as [(39 - 38.5) * 2/3] / (41.5 - 38.5) = 1/9. Therefore, the probability that a bag will weigh less than 39 pounds is 1/9 or \approx imately 0.11 or 11%. The probability that a bag will weigh between 39 and 40 pounds is the area under the probability density function from 39 to 40 pounds, which can be calculated as [(40 - 39) * 2/3] / (41.5 - 38.5) = 2/9. Therefore, the probability that a bag will weigh between 39 and 40 pounds is 2/9 or \approx imately 0.22 or 22%.