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Chapter 4: Q168SE (page 281)
Assume that xhas an exponential distribution with.
Find
a.
b.
c.
d.
e.
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Which of the following describe discrete random variables, and which describe continuous random variables?
a. The number of damaged inventory items
b. The average monthly sales revenue generated by a salesperson over the past year
c. Square feet of warehouse space a company rents
d. The length of time a firm must wait before its copying machine is fixed
Soft-drink dispenser. The manager of a local soft-drink bottling company believes that when a new beverage dispensing machine is set to dispense 7 ounces, it in fact dispenses an amount at random anywhere between 6.5and 7.5 ounces inclusive. Suppose has a uniform probability
distribution.
a.Is the amount dispensed by the beverage machine a discreteor a continuous random variable? Explain.
b. Graph the frequency function for , the amount of beverage the manager believes is dispensed by the new machine when it is set to dispense 7 ounces.
c. Find the mean and standard deviation for the distribution graphed in part b, and locate the mean and theinterval on the graph.
d. Find .
e. Find .
f. Find .
g. What is the probability that each of the next six bottles filled by the new machine will contain more than7.25 ounces of beverage? Assume that the amount of beverage dispensed in one bottle is independent of the amount dispensed in another bottle.
LASIK surgery complications. According to studies, 1% of all patients who undergo laser surgery (i.e., LASIK) to correct their vision have serious post laser vision problems (All About Vision, 2012). In a sample of 100,000 patients, what is the approximate probability that fewer than 950 will experience serious post laser vision problems?
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.
The random variable x has a normal distribution with and . Find a value of x, call it, such that
a.
b.
c.
d.
e.
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