A Manufacturing Company Has 5 Identical Machines That Produce Nails

question 119

Short Answer

A manufacturing company has 5 identical machines that produce nails. The probability that a machine will break down on any given day is .1. Define a random variable X to be the number of machines that will break down in a day.
a.What is the appropriate probability distribution for X? Explain how X satisfies the properties of the distribution.
b.Compute the probability that 4 machines will break down.
c.Compute the probability that at least 4 machines will break down.
d.What is the expected number of machines that will break down in a day?
e.What is the variance of the number of machines that will break down in a day?

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Definitions:

Cue-dependent Forgetting

The failure to recall information in the absence of specific cues or conditions that were present at the time of memory encoding.

Decay

The process through which information is lost over time when it is not used or rehearsed.

Proactive Interference

A phenomenon where older information prevents the recall of newer information, impacting memory retention.

Retroactive Interference

A memory phenomenon where newly learned information interferes with the recall of previously learned information.