New Semester Started Get 50% OFF Study Help! --h --m --s Claim Now

Question Answers

Textbooks

Find textbooks, questions and answers

Oops, something went wrong!

Change your search query and then try again

Result Not Found

Books FREE
Study Help
Tutors
AI Study Planner NEW
Sell Books

Search
Sign In
Register

study help
business
applied statistics and multivariate

Applied Statistics And Probability For Engineers 5th Edition Douglas C. Montgomery, George C. Runger - Solutions

Let the random variable X denote a measure- ment from a manufactured product. Suppose the target value for the measurement is w. For example, X could denote a dimensional length, and the target might be 10 millimeters. The quality loss of the process producing the product is defined to be the
A bearing assembly contains 10 bearings. The bearing diameters are assumed to be independent and normally distributed with a mean of 1.5 millimeters and a standard deviation of 0.025 millimeter. What is the probability that the maximum diameter bearing in the assembly exceeds 1.6 millimeters?
The steps in this exercise lead to the probabil- ity density function of an Erlang random variable X' with parameters and r, f(x) = x'x '^(-1),x>0. and = 1,2..... (a) Use the Poisson distribution to express P{X> x). (b) Use the result from part (a) to determine the cumu- lative distribution
Continuation of Exercise 4-176.Rework parts (a) and (b). Assume that the lifetime is a lognormal random vari- able with the same mean and standard deviation
Continuation of Exercise 4-176.Rework parts (a) and (b). Assume that the lifetime is an exponential random variable with the same mean.
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 5800 hours? (b) What is the life in hours that 90% of the lasers exceed? (c) What should the mean
Continuation of Exercise 4-174.Assume that the standard deviation of the size of a dot is 0.0004 inch. If the probability that a dot meets specifications is to be 0.9973, what specifications are needed? Assume that the specifications are to be chosen symmetrically around the mean of 0.002.
Suppose that X has a lognormal distribution with parameters = 0 and = 4.Determine the following: (a) P(10X50) (b) The value for x such that PX(e) The covering thickness of 95% of samples is below what value?
The CPU of a personal computer has a lifetime that is exponentially distributed with a mean lifetime of six years. You have owned this CPU for three years.(a) What is the probability that the CPU fails in the next three years? (b) Assume that your corporation has owned 10 CPUs for three years, and
The time between calls is exponentially distributed with a mean time between calls of 10 minutes. (a) What is the probability that the time until the first call is less than 5 minutes? (b) What is the probability that the time until the first call is between 5 and 15 minutes? (c) Determine the
Suppose that f(x)=05x-1 for 2 3) (c) P(2.5 <
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 for the lognormal distri- bution. (b) What is the probability of a particle size greater than 0.005
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) What is the probability that a pump will last longer than its mean?
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 distributed with a mean of 30 min- utes. Assume that each call orders one ticket. What is the prob
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 probability that more than 225 become ill (b) The probability that between 175 and 225 become ill
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 probability that a part is longer than 90.3 mil- limeters or shorter than 89.7 millimeters? (b) What should
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 less than 45 minutes? (b) What is the probability that it takes a cell more than 65 minutes to
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 males age 17 was 120.87 mm Hg. If the co- efficient of variation (100% x standard deviation mean) is
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 of the lognormal distribution. (b) Determine the probability that a lifetime exceeds 10,000 hours.
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 = exp(9) and y = exp(*) and write two equations in terms of x and y.)
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 page is viewed for more than 10 seconds?(b) By what length of time have 50% of the users moved to
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 X 1000 (c) What does the difference between the probabilities in parts (a) and (b) imply about
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 X represent the lifetime of a component in hours. Comment on the probability that the
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 in the previous parts com- pared to the results for an exponential distribution. (d) Comment on the
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 in the previous parts com- pared to the results for an exponential distribution.
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 wind speed at stations throughout the US. A Weibull distribution can be used to model the
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 ocean wave heights. Assume that the mean wave height at the observation station is 2.5 m and the shape
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 variance of the life of the MRI. (c) What is the probability that the MRI fails before 250 hours?
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 the life of the CPU. (c) What is the probability that the CPU fails before 500 hours?
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 the mean time until failure of a bearing. (c) If 10 bearings are in use and failures occur
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) Assume each step has the same distribution for service time. What distribution for each step and how
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 20 minutes is re- quired for the third arrival?
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 in 10 minutes? (b) What is the probability that the time until the fifth cus- tomer arrives is less
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 time between call numbers 50 and 80? (c) What is the probability that three or more calls occur
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 occur? (b) What is the standard deviation of the number of bits until five errors occur?(c) The
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 Poisson process with = 30 mes- sages per minute. Five messages are used to form a packet. (a) What is
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 probability that the time until the third failure exceeds 50,000 hours?
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 is the expected number of pounds of material required to obtain 15 particles of contamination? (b)
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 call? (b) What is the mean time until the tenth call? (c) What is the mean time between the ninth and
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 of the length of stay? (b) What is the probability of a length of stay greater than 10 hours? (c)
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 days. (a) What is the probability that the next change occurs in less than two days? (b) What is the
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) What is the probability that there are no flaws in 10 con- secutive meters of tape? (c) Does your
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 probability that there are no calls within one- half hour? (c) Determine x such that the
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? (b) If 30 separate one-hour intervals are chosen, what is the probability that no interval contains
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 highway? (b) What is the probability that there are two 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) What is the mean number of grams of chocolate until a fragment is detected? (b) What is the
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 are no sightings within three months (0.25 years)? (c) What is the probability that the time until
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 you have already been waiting for one hour for a taxi. What is the probability that one arrives
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 hours? (b) What proportion of the fans will last at most 7000 hours?
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 to own it for six years. (a) What is the probability that the voltage regulator fails during your
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 study region in central Phoenix, Arizona, recorded 10,500 asthma incidents in chil- dren in a
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 abundance from an operon (a set of biologically related genes) was less dispersed than from
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 each page independent random variables? (b) What is the mean number of pages with errors (one or
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 contains more than 10,000 particles?
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. The probability that an account has an error in a month is 0.001, and accounts can be assumed to be
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 over (http://factfinder.census.gov). A sample of 1000 persons is selected at random. (a) Approximate
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 defective. (b) Approximate the probability that between 20 and 30 chips are defective.
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 part (a). (c) Approximate the probability that 8 72) (b) P(X
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 than 90.(c) Approximate the probability that X = 80.
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 major oil- and gas-producing areas of western Canada. The mean monthly exposure to PM1.0 (par-
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. Suppose that the true weight of a sample is 165.5 grams. (a) What is the probability that the rounded
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? (b) What must the standard deviation of weight be in order for the company to state that 99.9% of
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 dot exceeds 0.0026 inch? (b) What is the probability that a diameter is between 0.0014 and 0.0026
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 5000 hours? (b) What is the life in hours that 95% of the lasers exceed? (c) If three lasers are used
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 with a mean of 310 million gallons per day and a standard deviation of 45 million gallons per day.
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 distribution with a mean of 1.41 cm and a standard deviation of 0.01 cm. (a) What is the probability
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 normally distributed with a standard de- viation of 2 inches. (a) What is the probability that a
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 deviation of 4 kilobits per second.(a) What is the probability that the file will transfer at a speed of
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 more than 0.5 seconds? (b) What is the probability that a reaction requires between 0.4 and 0.5
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 99.9% of all cans exceed 12 ounces? (b) At what value should the mean be set so that 99.9% of all cans
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) What is the probability that a fill volume is less than 12 fluid ounces? (b) If all cans less than
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 line width is greater than 0.62 micrometer? (b) What is the probability that a line width is between
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 it becomes discrete. Suppose that the true voltage is 250 millivolts. (a) What is the probability
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 time (in minutes)? (b) What is the probability that the message arrives less than 10 minutes before
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 cumulative distribution function of pho- toresist thickness. (b) Determine the proportion of wafers
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 op- erator to fill out the form? (b) What is the probability that it will take less than two min-
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 before failure.
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 <

Showing 1300 - 1400 of 2391

First
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
Last

Step by Step Answers

Services

Sitemap
Fun
Definitions
Become Tutor
Used Textbooks
Study Help Categories
Recent Questions
Expert Questions
Campus Wear
Sell Your Books

Company Info

Security
Copyrights
Privacy Policy
Terms & Conditions
SolutionInn Fee
Scholarship
Online Quiz
Give Feedback, Get Rewards

Get In Touch

About Us
Contact Us
Career
Jobs
FAQ
Student Discount
Campus Ambassador

Secure Payment

Download Our App

© 2026 SolutionInn. All Rights Reserved