Question

A center-pivot sprinkler system operated by Colorado Land & Agriculture, Inc., is used to water the alfalfa in a circular field. The circumference of the field is 2 miles. As the sprinkler travels in an arc around the field, sprinkler nozzles get clogged and must be cleaned. The distance around the circumference of the field from the starting point to the point when a nozzle becomes clogged is the value of a random variable X that is uniformly distributed over the 2-mile circumference of the field. As a part of a simulation comparing farm maintenance policies, an input is the point at which sprinklers become clogged. If a random number 0.724 is generated, at what distance from the starting point would we simulate that a nozzle becomes clogged? Give your answer to 3 decimal places.

Answer 1

The answer is "1.448 miles".

Explanation:

X= The distance to both the nozzle clogged from of the starting point.

X
`\sim` Uniform(0,2) miles.

They are simulating the random number Y=0.724, and the Y has both a distribution uniform(0,1). Therefore 2Y is distributed evenly (0.2). And They model the clogging of its nozzle at 2Y=1.448 miles