Applied Statistics and Probability for Engineers 6th Edition solutions

Applied Statistics and Probability for Engineers 6
Use Appendix Table III to determine the following probabilities for the standard normal random variable Z: (a) P(Z ,1.32) (b) P(Z ,3.0) (c) P(Z .1.45) (d) P(Z .? 2.15) (e) P(? 2.34,Z ,1.76)

Applied Statistics and Probability for Engineers 6
Use Appendix Table III to determine the following probabilities for the standard normal random variable Z: (a) P(? 1?Z ?1) (b) P(? 2?Z ?2) (c) P(? 3?Z ?3) (d) P(Z ?3) (e) P(0?Z ?1)

Applied Statistics and Probability for Engineers 6
Assume that Z has a standard normal distribution. Use Appendix Table III to determine the value for z that solves each of the following: (a) P(Z ?z) = 0.9 (b) P(Z ?z) = 0.5 (c) P(Z ?z) = 0.1 (d) P(Z ?z) = 0.9 (e) P(?1.24? Z ? z) = 0.8

Applied Statistics and Probability for Engineers 6
Assume that Z has a standard normal distribution. Use Appendix Table III to determine the value for z that solves each of the following: (a) P(?z?Z ?z) = 0.95 (b) P(?z?Z ?z) = 0.99 (c) P(?z?Z ?z) = 0.68 (d) P(?z?Z ?z) = 0.9973

Applied Statistics and Probability for Engineers 6
Assume that X is normally distributed with a mean of 10 and a standard deviation of 2. Determine the following: (a) \(P(Z, 13)\) (b) \(P(Z .9)\) (c) \(P(6, X, 14)\) (d) \(P(2, X, 4)\) (e) \(P(-2, X, 8)\) Equation transcription: Text transcription: P(Z, 1

Applied Statistics and Probability for Engineers 6
Assume that X is normally distributed with a mean of 10 and a standard deviation of 2. Determine the value for x that solves each of the following: (a) \(P(X>x)=0.5\) (b) \(P(X>x)=0.95\) (c) \(P(x<X<10)=0\) (d) \(P(-x<X-10<x)=0.95\)

Applied Statistics and Probability for Engineers 6
Assume that X is normally distributed with a mean of 5 and a standard deviation of 4. Determine the following: (a) P(X < 11) (b) P(X > 0) (c) P(3 < X < 7) (d) P(-2 < X < 9) (e) P(2 < X < 8)

Applied Statistics and Probability for Engineers 6
Assume that X is normally distributed with a mean of 5 and a standard deviation of 4. Determine the value for x that solves each of the following: (a) \(P(X>x)=0.5\) (b) \(P(X>x)=0.95\) (c) \(P(x<X<9)=0.2\) (d) \(P(3<X<x)=0.95\) (e) \(P(-x<X-5<x)=0.99\)

Applied Statistics and Probability for Engineers 6
Problem 71E The compressive strength of samples of cement can be modeled by a normal distribution with a mean of 6000 kilograms per square centimeter and a standard deviation of 100 kilograms per square centimeter. (a) What is the probability that a samples strength is less than 6250 Kg/cm2? (b) What

Applied Statistics and Probability for Engineers 6
Problem 72E The time until recharge for a battery in a laptop computer under common conditions is normally distributed with a mean of 260 minutes and a standard deviation of 50 minutes. (a) What is the probability that a battery lasts more than four hours? (b) What are the quartiles (the 25% and 75%

Applied Statistics and Probability for Engineers 6
Problem 73E An article in Knee Surgery Sports Traumatol Arthrosc [Effect of Provider Volume on Resource Utilization for Surgical Procedures (2005, Vol. 13, pp. 273279)] showed a mean time of 129 minutes and a standard deviation of 14 minutes for anterior cruciate ligament (ACL) reconstruction surgery

Applied Statistics and Probability for Engineers 6
Cholesterol is a fatty substance that is an important part of the outer lining (membrane) of cells in the body of animals. Its normal range for an adult is 120240 mg/dl. The Food and Nutrition Institute of the Philippines found that the total cholesterol level for Filipino adults has a mean of 159.2

Applied Statistics and Probability for Engineers 6
Problem 75E The line width for semiconductor manufacturing is assumed to be normally distributed with a mean of 0.5 micrometer 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 b

Applied Statistics and Probability for Engineers 6
Problem 76E 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 l

Applied Statistics and Probability for Engineers 6
Problem 77E In the previous exercise, suppose that the mean of the filling operation can be adjusted easily, but the standard deviation remains at 0.1 fluid ounce. (a) At what value should the mean be set so that 99.9% of all cans exceed 12 fluid ounces? (b) At what value should the mean be set so th

Applied Statistics and Probability for Engineers 6
Problem 78E A drivers reaction time to visual stimulus is normally 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 seco

Applied Statistics and Probability for Engineers 6
Problem 79E The speed of a file transfer from a server on campus to a personal computer at a students home on a weekday evening is normally distributed with a mean of 60 kilobits per second and a standard deviation of four kilobits per second. (a) What is the probability that the file will transfer a

Applied Statistics and Probability for Engineers 6
Problem 80E In 2002, the average height of a woman aged 2074 years was 64 inches with an increase of approximately 1 inch from 1960 (http://usgovinfo.about.com/od/healthcare). Suppose the height of a woman is normally distributed with a standard deviation of two inches. (a) What is the probability th

Applied Statistics and Probability for Engineers 6
Problem 81E In an accelerator center, an experiment needs a 1.41-cmthick aluminum cylinder (http://puhep1.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 proba

Applied Statistics and Probability for Engineers 6
Problem 82E The demand for water use in Phoenix in 2003 hit a high of about 442 million gallons per day on June 27 (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 da

Applied Statistics and Probability for Engineers 6
Problem 83E The life of a semiconductor laser at a constant power is normally distributed with a mean of 7000 hours and a standard 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

Applied Statistics and Probability for Engineers 6
Problem 84E The diameter of the dot produced by a printer is normally 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? (b) What is the probability that a diameter is between 0.0014 and 0.0026

Applied Statistics and Probability for Engineers 6
The weight of a sophisticated running shoe is normally 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 its

Applied Statistics and Probability for Engineers 6
Measurement error that is normally distributed with a mean of 0 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 resu

Applied Statistics and Probability for Engineers 6
Assume that a random variable is normally distributed with a mean of 24 and a standard deviation of 2. Consider an interval of length one unit that starts at the value a so that the interval is [a, a + 1]. For what value of a is the probability of the interval greatest? Does the standard deviation af

Applied Statistics and Probability for Engineers 6
Problem 88E A study by Bechtel et al., 2009, described in the Archives of Environmental & 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

Applied Statistics and Probability for Engineers 6
Problem 89E An article in Atmospheric Chemistry and Physics Relationship Between Particulate Matter and Childhood Asthma Basis of a Future Warning System for Central Phoenix (2012, Vol. 12, pp. 24792490)] reported the use of PM10 (particulate matter ??10 ?m diameter) air quality data measured hourly

Applied Statistics and Probability for Engineers 6
Problem 90E 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 2.9. Assume that the length of stay is normally distributed. (a) What is the probability of a length of stay greater than 10 hours? (b) What length of st

Applied Statistics and Probability for Engineers 6
Problem 91E A signal in a communication channel is detected when the voltage is higher than 1.5 volts in absolute value. Assume that the voltage is normally distributed with a mean of 0. What is the standard deviation of voltage such that the probability of a false signal is 0.005?

Applied Statistics and Probability for Engineers 6
Problem 92E An article in Microelectronics Reliability [Advanced Electronic Prognostics through System Telemetry and Pattern Recognition Methods (2007, Vol.47(12), pp. 18651873)] presented an example of electronic prognosis. The objective was to detect faults to decrease the system downtime and the n

Applied Statistics and Probability for Engineers 6
Problem 93E An article in International Journal of Electrical Power & Energy Systems [Stochastic Optimal Load Flow Using a Combined QuasiNewton and Conjugate Gradient Technique (1989, Vol.11(2), pp. 8593)] considered the problem of optimal power flow in electric power systems and included the effects

Applied Statistics and Probability for Engineers 6
Problem 94E An article in the Journal of Cardiovascular Magnetic Resonance [Right Ventricular Ejection Fraction Is Better Reflected by Transverse Rather Than Longitudinal Wall Motion in Pulmonary Hypertension (2010, Vol.12(35)] discussed a study of the regional right ventricle transverse wall motion