ICA4
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School
North Carolina State University *
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Course
515
Subject
Industrial Engineering
Date
Dec 6, 2023
Type
docx
Pages
4
Uploaded by CaptainTapir2529
A company producing orange juice buys all its oranges from a large orange
orchard. The amount of juice that can be squeezed from each of these
oranges is approximately normally distributed with a mean of 4.7 ounces
and some unknown standard deviation. The company's production
manager knows that the probability is 30.85% that a randomly selected
orange will contain less than 4.5 ounces of juice. Also the probability is
10.56% that a randomly selected orange will contain more than 5.2 ounces
of juice.
a.
what is the probability that a randomly selected orange will contain
between 4.5 and 5.2 ounces of juices?
b.
what is the probability that a randomly selected orange will contain at
least 4.9 ounces of juices?
c.
what is the probability that a randomly selected orange will contain
no more than 4.9 ounces of juices?
The FICO credit score on a certain nationwide credit card follows a normal
distribution with a mean of 500 and a standard deviation of 100. It is known that a
credit carder holder is a Platinum customer if his/her FICO score is over 650.
Suppose 500 credit card holders are randomly drawn from the population. What is
the probability that at least 50 of them are Platinum customers?
Suppose that the wrapper of a certain candy bar lists its weight as 2.13 ounces.
Suppose that the actual weights of these candy bars vary according to a normal
distribution with mean μ = 2.2 ounces and variance 0.0036 ounces.
a.
In a random sample of 5 candy bars, what is the probability that at least one
of the candy bars weighs less than the advertised weight?
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b.
If the manufacturer wants to adjust the production process so that only 1
candy bar in 100 weighs less than the advertised weight, what should the
mean of the actual weights be (assuming that the variance of the weights
remains 0.0036 ounces)?