QA 233 (Basic
Business Statistics)
Practice Problems
V
- Chapter 5
Pillar
Foods, Inc. produces Choco-Poofies, a breakfast cereal popular with young
children. They currently produce ten ounce, twenty ounce, and three pound
(thirty-six ounce economy size) boxes of this cereal. After a slurry of the
ingredients is mixed, it is extruded through a star-shaped mold, cut into
quarter-inch wide pieces, and baked until crunchy. Every production employee has
the capability of bringing production to an immediate stop if he/she observes a
problem with the process. Once the baking process is complete, the final product
is brought by conveyor belt into machines that funnel the product into boxes. A
ticket with a point value of 1, 2, 3, 4, or 5 (redeemable for a plastic giraffe,
a plastic elephant, a plastic hippopotamus, a plastic three-toed sloth, or a
plastic hyena once a certain number of points is accumulated) is then dropped
into the box, and the box is sealed.
-
Suppose
that the average number of times the production process is stopped by an
employee throughout a single shift (eight hours) is 3.5. What is the
probability that the process will not be stopped during a one-hour period?
What is the probability that the process will be stopped at least twice
during a one-hour period? - QA 233 Students - only
identify what type of distribution would describe the random variable in
this problem!
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If
tickets of the various point values (1, 2, 3, 4, 5) are distributed
throughout the boxes evenly, what is the probability that a randomly
selected box will include a ticket with a point value of at least four?
Under these conditions, what is the probability that a randomly selected
box will include a ticket with a point value of no more than two?
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Again
assume the conditions outlined in problem 2 (tickets of each point value
are equally likely) are true. If you randomly select twelve boxes of
Choco-Poofies, what is the probability that at least three of the boxes
will contain a five-point ticket? What is the probability that none of the
boxes will contain a one-point ticket?
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Each
day Pillar Foods randomly selects ten of their 1250 production employees
to perform quality control inspections throughout the production process.
In order to cover all quality control-related tasks, at least eight of the
ten randomly selected employees must be at work on that day. If the
probability that any worker will call in sick on a given day is 0.05, what
is the probability Pillar Foods will not have enough employees from the
ten who have been randomly selected to perform their quality control tasks
(i.e., that at least two of the selected workers will call in sick on a
given day)?
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