The amount of timber harvested and sold is associated with the housing market and the general economy. In 2012, the total amount of timber harvested in the United States was 2,500,321 mbf (thousand...


The amount of timber harvested and sold is associated with the housing market and the general economy. In 2012, the total amount of timber harvested in the United States was 2,500,321 mbf (thousand board feet).14 It takes approximately 11 mbf to construct a typical 1900-square-foot-home. Assume the volume of timber harvested per acre is normally distributed with mean 30 mbf and standard deviation 6.25 mbf. Suppose an acre of timber is selected at random.


 a. What is the probability that the volume of timber harvested is between 25 and 40 mbf?


b. What is the probability that the volume of timber harvested is less than 20 mbf?


c. Suppose the acre has already produced 35 mbf. What is the probability that the volume harvested will be more than 40 mbf?


 d. A logging company selects three random acres to harvest during a week. The company will make a profit if all three acres produce more than 32 mbf. What is the probability that the logging company makes a profit?


Kraft Foods recently announced that the Kool-Aid mascot, that big red pitcher of the powdered drink mix with arms and legs, will receive a makeover as they unveil a new liquid mix. Kool-Aid bursts are distributed in various flavors including tropical punch, berry blue, and grape. Kraft Foods claims that the mean amount of Kool-Aid in each burst bottle is 200 milliliters (ml).15 Assume the amount of drink in each bottle is normally distributed with standard deviation 1.25 ml. Suppose a bottle of berry blue is selected at random.


a. What is the probability that the amount of drink will be between 199 and 201 ml?


b. If the amount of drink is more than 202 ml, when the bottle is opened there will be a spill. What is the probability of a spill?


c. Suppose there are 196 ml in the bottle of berry blue. Is there any evidence to suggest the claim made by Kraft Foods is false? Justify your answer.

May 04, 2022
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