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applied statistics and multivariate

Questions and Answers of Applied Statistics And Multivariate

The size of silver particles in a photographic emul- sion is known to have a log normal distribution with a mean of 0.001 mm and a standard deviation of 0.002 mm. (a) Determine the parameter values
The life of a recirculating pump follows a Weibull distribution with parameters = 2 and 8 = 700 hours. (a) Determine the mean life of a pump. (b) Determine the variance of the life of a pump. (c)
When a bus service reduces fares, a particular trip from New York City to Albany, New York, is very popular. A small bus can carry four passengers. The time between calls for tickets is exponentially
The percentage of people exposed to a bacteria who become illis 20%. Assume that people are independent. Assume that 1000 people are exposed to the bacteria. Approximate each of the following: (a)
The length of an injection-molded plastic case that holds magnetic tape is normally distributed with a length of 90.2 millimeters and a standard deviation of 0.1 millimeter. (a) What is the
The time it takes a cell to divide (called mitosis) is normally distributed with an average time of one hour and a standard deviation of 5 minutes. (a) What is the probability that a cell divides in
Suppose the length of stay (in hours) at an emergency department is modeled with a lognormal random variable X with 8 1.5 and 0.4.Determine the following (a) mean and variance (b) P(X
Suppose X has a lognormal distribution with param- eters 10 and 16.Determine the following: (a) P(X 1500) (c) value exceeded with probability 0.7
An article in Health and Population: Perspectives and Issues (2000, Vol. 23, pp. 28-36) used the lognormal distribution to model blood pressure in humans. The mean systolic blood pressure (SBP) in
The lifetime of a semiconductor laser has a lognor mal distribution, and it is known that the mean and standard deviation of lifetime are 10,000 and 20,000, respectively. (a) Calculate the parameters
Suppose that Xhas a lognormal distribution and that the mean and variance of X are 100 and 85,000, respectively. Determine the parameters and w of the lognormal distribu- tion. (Hint: define x =
The length of time (in seconds) that a user views a page on a Web site before moving to another page is a lognor mal random variable with parameters = 0.5 and s = 1.(a) What is the probability that a
Suppose that X has a lognormal distribution with parameters = -2 and w-9. Determine the following: (a) P(500X1000) (b) The value for x such that P(X(a) P(X < 500) (b) The conditional probability that
Suppose that X has a lognormal distribution with parameters = 5 and =9. Determine the following: (a) P(X < 13,300) (b) The value for x such that P(X = x) = 0.95 (c) The mean and variance of X
Suppose X has a Weibull distribution with B = 2 and 8 = 2000.(a) Determine PCX> 3500). (b) Determine PX>3500) for an exponential random vari able with the same mean as the Weibull distribution. (c)
Suppose the lifetime of a component (in hours) is modeled with a Weibull distribution with = 0.5 and 8 4000. Determine the following: (a) P(X3000) (b) PLX> 6000X3000) (c) Comment on the probabilities
Suppose the lifetime of a component (in hours) is modeled with a Weibull distribution with = 2 and 8 = 4000. Determine the following: (a) PX3000) (b) PLY> 6000X3000) (c) Comment on the probabilities
Suppose that Xhas a Weibull distribution with B-2 and & 8.6.Determine the following: (a) P(X 9) (c) P(8 < x) = 0.9
An article in the Journal of Geophysical Research ["Spatial and Temporal Distributions of US. of Winds and Wind Power at 80 m Derived from Measurements," (2003, vol. 108, pp. 10-1: 10-20)] considered
An article in the Journal of the Indian Geophysical Union titled "Weibull and Gamma Distributions for Wave Parameter Predictions" (2005, Vol. 9, pp. 55-64) used the Weibull distribution to model
The life (in hours) of a magnetic resonance imaging machine (MRI) is modeled by a Weibull distribution with pa- rameters B 2 and 6 500 hours. (a) Determine the mean life of the MRI. (b) Determine the
The life (in hours) of a computer processing unit (CPU) is modeled by a Weibull distribution with parameters B=3 and & 900 hours. (a) Determine the mean life of the CPU (b) Determine the variance of
Assume that the life of a roller bearing follows a Weibull distribution with parameters = 2 and 8 = 10,000 hours. (a) Determine the probability that a bearing lasts at least 8000 hours. (b) Determine
If X is a Weibull random variable with = 1 and 8=1000, what is another name for the distribution of X and what is the mean of X?
Suppose that X has a Weibull distribution with = 0.2 and 8 = 100 hours. Determine the following: (a) P(X10,000) (b) P(X> 5000)
Suppose that X has a Weibull distribution with B=0.2 and 8=100 hours. Determine the mean and vari- ance of X.
The total service time of a multistep manufacturing operation has a gamma distribution with mean 18 minutes and standard deviation 6.(a) Determine the parameters A and 7 of the distribution. (b)
Patients arrive at an emergency department accord- ing to a Poisson process with a mean of 6.5 per hour. (a) What is the mean time until the tenth arrival? (b) What is the probability that more than
Show that the gamma density function {x, A. r) in- tegrates to 1.
Use integration by parts to show that F(r)=(-1) F(-1).
The time between arrivals of customers at an auto- matic teller machine is an exponential random variable with a mean of 5 minutes. (a) What is the probability that more than three customers arrive
Calls to the help line of a large computer distributor follow a Poisson distribution with a mean of 20 calls per minute. (a) What is the mean time until the one-hundredth call? (b) What is the mean
Errors caused by contamination on optical disks occur at the rate of one error every 10 bits. Assume the errors follow a Poisson distribution. (a) What is the mean number of bits until five emors
In a data communication system, several messages that arrive at a node are bundled into a packet before they are transmitted over the network. Assume the messages arrive at the node according to a
The time between failures of a laser in a cytogenics ma- chine is exponentially distributed with a mean of 25,000 hours. (a) What is the expected time until the second failure? (b) What is the
Raw materials are studied for contamination. Suppose that the number of particles of contamination per pound of material is a Poisson random variable with a mean of 0.01 particle per pound. (a) What
Calls to a telephone system follow a Poisson distri- bution with a mean of five calls per minute. (a) What is the name applied to the distribution and parame ter values of the time until the tenth
Given the probability density function f(x)= 0.013), determine the mean and variance of the distribution.
The length of stay at a specific emergency depart- ment in Phoenix, Arizona, had a mean of 4.6 hours. Assume that the length of stay is exponentially distributed. (a) What is the standard deviation
Web crawlers need to estimate the frequency of changes to Web sites to maintain a current index for Web searches. Assume that the changes to a Web site follow a Poisson process with a mean of 3.5
If the random variable Xhas an exponential distribu- tion with mean 0, determine the following: (a) P(X>0) (c) P(X>30) (b) P(X > 20) (d) How do the results depend on #?
Assume that the flaws along a magnetic tape follow a Poisson distribution with a mean of 0.2 flaw per meter. Let X denote the distance between two successive flaws. (a) What is the mean of X? (b)
The time between calls to a corporate office is expo- nentially distributed with a mean of 10 minutes. (a) What is the probability that there are more than three calls in one-half hour? (b) What is
The time between arrivals of small aircraft at a county airport is exponentially distributed with a mean of one hour. (a) What is the probability that more than three aircraft arrive within an hour?
The distance between major cracks in a highway fol- lows an exponential distribution with a mean of 5 miles. (a) What is the probability that there are no major cracks in a 10-mile stretch of the
According to results from the analysis of chocolate bars in Chapter 3, the mean number of insect fragments was 14.4 in 225 grams. Assume the number of fragments follows a Poisson distribution. (a)
The number of stork sightings on a route in South Carolina follows a Poisson process with a mean of 2.3 per year. (a) What is the mean time between sightings? (b) What is the probability that there
The time between arrivals of taxis at a busy intersec- tion is exponentially distributed with a mean of 10 minutes.(a) What is the probability that you wait longer than one hour a taxi? for (b)
Suppose that the time to failure (in hours) of fans in a personal computer can be modeled by an exponential distribu- tion with A = 0.0003. (a) What proportion of the fans will last at least 10,000
The life of automobile voltage regulators has an expo- nential distribution with a mean life of six years. You purchase an automobile that is six years old, with a working voltage regulator, and plan
Suppose X has an exponential distribution with A = 2.Determine the following: (a) PX0) (b) P(X2) (c) P1) (d) P(1 <
An article under review for Air Quality, Atmosphere & Health titled "Linking Particulate Matter (PM10) and Childhood Asthma in Central Phoenix" linked air quality to childhood asthma incidents. The
An acticle in Biometrics Integrative Analysis of Transcriptomic and Proteomic Data of Desulfovibrio vulgaris: A Nonlinear Model to Predict Abundance of Undetected Proteins" (2009)] found that protein
A high-volume printer produces minor print-quality errors on a test pattern of 1000 pages of text according to a Poisson distribution with a mean of 0.4 per page. (a) Why are the numbers of errors on
Suppose that the number of asbestos particles in a sample of 1 squared centimeter of dust is a Poisson random variable with a mean of 1000. What is the probability that 10 squared centimeters of dust
A corporate Web site contains errors on 50 of 1000 pages. If 100 pages are sampled randomly, without replace- ment, approximate the probability that at least 1 of the pages in error is in the sample.
Phoenix water is provided to approximately 1.4 million people, who are served through more than 362.000 accounts (http://phoenix.gov/WATER/wtrfacts.html). All accounts are metered and billed monthly.
There were 49.7 million people with some type of long-lasting condition or disability living in the United States in 2000. This represented 19.3 percent of the majority of civilians aged five and
The manufacturing of semiconductor chips produces 2% defective chips. Assume the chips are independent and that a lot contains 1000 chips. (a) Approximate the probability that more than 25 chips are
Suppose that X is a Poisson random variable with A = 6.(a) Compute the exact probability that Y is less than 4.(b) Approximate the probability that X is less than 4 and com- pare to the result in
Suppose that X is a binomial random variable with =200 and p=0.4. (a) Approximate the probability that X is less than or equal to 70.(b) Approximate the probability that X is greater than 70 and less
The length of stay at a specific emergency department in Phoenix, Arizona, in 2009 had a mean of 4.6 hours with a standard deviation of
A study by Bechtel, et al., 2009, in the Archives of Emironmental & Occupational Health considered polycyclic aromatic hydrocarbons and immune system function in beef cattle. Some cattle were near
Measurement error that is normally distributed with a mean of zero and a standard deviation of 0.5 gram is added to the true weight of a sample. Then the measurement is rounded to the nearest gram.
The weight of a sophisticated running shoe is nor mally distributed with a mean of 12 ounces and a standard deviation of 0.5 ounce. (a) What is the probability that a shoe weighs more than 13 ounces?
The diameter of the dot produced by a printer is nor- mally distributed with a mean diameter of 0.002 inch and a standard deviation of 0.0004 inch. (a) What is the probability that the diameter of a
The life of a semiconductor laser at a constant power is normally distributed with a mean of 7000 hours and a stan dard deviation of 600 hours. (a) What is the probability that a laser fails before
The demand for water use in Phoenix in 2003 hit a high of about 442 million gallons per day on June 27, 2003 (http://phoenix.gov/WATER/wtrfacts.html). Water use in the summer is normally distributed
In an accelerator center, an experiment needs a 1.41-cm- thick aluminum cylinder (http://pahep1.princeton.edu/mumu target/Solenoid Coil pdf). Suppose that the thickness of a cylinder has a normal
The average height of a woman aged 20-74 years is 64 inches in 2002, with an increase of approximately one inch from 1960 (http://usgovinfo.about.com/od/healthcare). Suppose the height of a woman is
The speed of a file transfer from a server on campus to a personal computer at a student's home on a weekday evening is normally distributed with a mean of 60 kilobits per second and a standard
The reaction time of a driver to visual stimulus is nor- mally distributed with a mean of 0.4 seconds and a standard deviation of 0.05 seconds. (a) What is the probability that a reaction requires
In the previous exercise, suppose that the mean of the filling operation can be adjusted easily, but the standard devi- ation remains at 0.1 ounce. (a) At what value should the mean be set so that
The fill volume of an automated filling machine used for filling cans of carbonated beverage is normally distributed with a mean of 12.4 fluid ounces and a standard deviation of 0.1 fluid ounce. (a)
The line width for semiconductor manufacturing is assumed to be normally distributed with a mean of 0.5 micro- meter and a standard deviation of 0.05 micrometer. (a) What is the probability that a
Measurement error that is continuous and uniformly distributed from -3 to +3 millivolts is added to the true voltage of a circuit. Then the measurement is rounded to the nearest mil- livolt so that
An e-mail message will arrive at a time uniformly distributed between 9:00 AM. and 11:00 AM. You check e-mail at 9:15 AM. and every 30 minutes afterward. (a) What is the standard deviation of arrival
The thickness of photoresist applied to wafers in semiconductor manufacturing at a particular location on the wafer is uniformly distributed between 0.2050 and 0.2150 micrometers. (a) Determine the
Suppose the time it takes a data collection operator to fill out an electronic form for a database is uniformly between 1.5 and 2.2 minutes. (a) What is the mean and variance of the time it takes an
Suppose X has a continuous uniform distribution over the interval [-1,1]. (a) Determine the mean, variance, and standard deviation of X. (b) Determine the value for x such that P(-x
Suppose X has a continuous uniform distribution over the interval [1.5, 5.5] (a) Determine the mean, variance, and standard deviation of X. (b) What is P(X
The thickness of a conductive coating in micrometers has a density function of 600x for 100 m
The gap width is an important property of a magnetic recording head. In coded units, if the width is a continuous random variable over the range from 0 0
The probability density function of the time customers arrive at a terminal (in minutes after 8:00 A.M.) is f(x) = 10/10 for probability that the first customer arrives between 8:15 A.M. and 8:30 AM.
Determine the cumulative distribution function for the distribution in Exercise 4-8.Use the cumulative distribu- tion function to determine the probability that a component lasts more than 3000 hours
Determine the cumulative distribution function for the distribution in Exercise 4.5.
Determine the cumulative distribution function for the distribution in Exercise 4.4.
Determine the cumulative distribution function for the distribution in Exercise 4-1.
Suppose the cumulative distribution function of the random variable X is x -1.5) (c) PX-2) (d) P(-1 <
Suppose the cumulative distribution function of the random variable X is x
The probability density function of the length of a metal rod is f(x) = 2 for 23
The probability density function of the length of a cut- ting blade isf(x) = 1.25 for 74.6 75.2) (c) If the specifications for this process are from 74.7 to 75.3 millimeters, what proportion of
The probability density function of the net weight in pounds of a packaged chemical herbicide is f(x) = 2.0 for 49.75 x50.25 pounds. (a) Determine the probability that a package weighs more than 50
Approximate probabilities for some binomial and Poisson distributions
Use the table for the cumulative distribution function of a standard normal distribution to calculate probabilities
Standardize normal random variables
Calculate probabilities, determine means and variances for some common continuous probability distributions
Select an appropriate continuous probability distribution to calculate probabilities in specific applications
Understand the assumptions for some common continuous probability distributions
Calculate means and variances for continuous random variables

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