In the construction process for solid-state flash memory drives (thumb drives), nearly all drives are constructed with a large potential amount of storage space, and are sold base on the actual amount of memory that forms correctly during the process (For example, drives that are designed to store 64 gb but contain a large number of bad sectors will instead be formated and sold as 32 gb). Consider a manufacturing process where every chip has a 21% of having enough bad sectors to be downgraded, and these errors are random and independent.

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4. Probability Distributions
In the construction process for solid-state flash memory drives (thumb drives), nearly all drives are
constructed with a large potential amount of storage space, and are sold base on the actual amount
of memory that forms correctly during the process (For example, drives that are designed to store 64
gb but contain a large number of bad sectors will instead be formated and sold as 32 gb). Consider a
manufacturing process where every chip has a 21% of having enough bad sectors to be downgraded,
and these errors are random and independent.
(a) If we wish to compute the probability that z number of chips out of a production run of size n are
downgraded, do we have a probability distribution that will work for that? Are the assumptions
for that met? Explain.
(b) Compute the probability that 5 chips out of a production run of 40 are downgraded.
(c) Compute the probability that between 3 and 5 (inclusive) or between 2 and 8 (inclusive) are
downgraded.
(d) Graph the probability mass function for r number of chips out of a production run of 10 are
downgraded.
Transcribed Image Text:4. Probability Distributions In the construction process for solid-state flash memory drives (thumb drives), nearly all drives are constructed with a large potential amount of storage space, and are sold base on the actual amount of memory that forms correctly during the process (For example, drives that are designed to store 64 gb but contain a large number of bad sectors will instead be formated and sold as 32 gb). Consider a manufacturing process where every chip has a 21% of having enough bad sectors to be downgraded, and these errors are random and independent. (a) If we wish to compute the probability that z number of chips out of a production run of size n are downgraded, do we have a probability distribution that will work for that? Are the assumptions for that met? Explain. (b) Compute the probability that 5 chips out of a production run of 40 are downgraded. (c) Compute the probability that between 3 and 5 (inclusive) or between 2 and 8 (inclusive) are downgraded. (d) Graph the probability mass function for r number of chips out of a production run of 10 are downgraded.
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