Learning Materials
Features
Discover
Chapter 4: Q169SE (page 281)
The random variable xhas a normal distribution withand . Find the following probabilities:
a.
b.
c.
d.
e.
f.
a.
b.
c.
d.
e.
f.
Over 30 million students worldwide already upgrade their learning with 91影视!
All the tools & learning materials you need for study success - in one app.
Get started for free
The random variable x has a normal distribution with and . Find a value of x, call it, such that
a.
b.
c.
d.
e.
Box plots and the standard normal distribution. What relationship exists between the standard normal distribution and the box-plot methodology (Section 2.8) for describing distributions of data using quartiles? The answer depends on the true underlying probability distribution of the data. Assume for the remainder of this exercise that the distribution is normal.
a. Calculate the values of the standard normal random variable z, call them zL and zU, that correspond to the hinges of the box plot鈥攖hat is, the lower and upper quartiles, QL and QU鈥攐f the probability distribution.
b. Calculate the zvalues that correspond to the inner fences of the box plot for a normal probability distribution.
c. Calculate the zvalues that correspond to the outer fences of the box plot for a normal probability distribution.
d. What is the probability that observation lies beyond the inner fences of a normal probability distribution? The outer fences?
e. Can you better understand why the inner and outer fences of a box plot are used to detect outliers in a distribution? Explain.
Industrial filling process. The characteristics of an industrialfilling process in which an expensive liquid is injectedinto a container were investigated in the Journal of QualityTechnology(July 1999). The quantity injected per containeris approximately normally distributed with mean 10
units and standard deviation .2 units. Each unit of fill costs\(20 per unit. If a container contains less than 10 units (i.e.,is underfilled), it must be reprocessed at a cost of \)10. A properly filled container sells for $230.
a. Find the probability that a container is underfilled. Notunderfilled.
b. A container is initially underfilled and must be reprocessed.Upon refilling, it contains 10.60 units. Howmuch profit will the company make on thiscontainer?
c. The operations manager adjusts the mean of the fillingprocess upward to 10.60 units in order to makethe probability of underfilling approximately zero.
Under these conditions, what is the expected profit percontainer?
Shear strength of rock fractures. Understanding the characteristics
of rock masses, especially the nature of the fracturesis essential when building dams and power plants.The shear strength of rock fractures was investigated inEngineering Geology(May 12, 2010). The Joint RoughnessCoefficient (JRC) was used to measure shear strength.Civil engineers collected JRC data for over 750 rock fractures.The results (simulated from information provided in the article) are summarized in the accompanying SPSShistogram. Should the engineers use the normal probabilitydistribution to model the behavior of shear strength forrock fractures? Explain
Hospital patient interarrival times. The length of time between arrivals at a hospital clinic has an approximately exponential probability distribution. Suppose the mean time between arrivals for patients at a clinic is 4 minutes.
a. What is the probability that a particular interarrival time (the time between the arrival of two patients) is less than 1 minute?
b. What is the probability that the next four interarrival times are all less than 1 minute?
c. What is the probability that an interarrival time will exceed 10 minutes?
What do you think about this solution?
We value your feedback to improve our textbook solutions.
Explanations 
Textbooks 
Flashcards 
91影视 AI 
Notes 
Study Plans 
Study Sets 
Find a degree 
Magazine