
Applied Statistics and Probability for Engineers
6th Edition
ISBN: 9781118539712
Author: Douglas C. Montgomery
Publisher: WILEY
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Chapter 4.10, Problem 160E
To determine
Find the standard deviation of the wave weight.
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You want to obtain a sample to estimate the proportion of a population that possess a particular genetic marker. Based on previous evidence, you believe approximately p∗=11% of the population have the genetic marker. You would like to be 90% confident that your estimate is within 0.5% of the true population proportion. How large of a sample size is required?n = (Wrong: 10,603)
Do not round mid-calculation. However, you may use a critical value accurate to three decimal places.
Chapter 4 Solutions
Applied Statistics and Probability for Engineers
Ch. 4.2 - 4-1. Suppose that f(x) = e−x for 0 < x. Determine...Ch. 4.2 - 4-2. Suppose that f (x) = 3(8x – x2)/256 for 0< x...Ch. 4.2 - 4-3. Suppose that f (x) = 0.5 cos x for −π/2 < x <...Ch. 4.2 - Prob. 4ECh. 4.2 - 4-5. Go Tutorial Suppose that for 3 < x < 5....Ch. 4.2 - Prob. 6ECh. 4.2 - 4-7. Suppose that f(x) = 1 .5x2 for −1 < x < 1....Ch. 4.2 - 4-8. The probability density function of the time...Ch. 4.2 - 4-9. The probability density function of the net...Ch. 4.2 - Prob. 10E
Ch. 4.2 - 4-11. The probability density function of the...Ch. 4.2 - Prob. 12ECh. 4.2 - 4-13. A test instrument needs to be calibrated...Ch. 4.2 - Prob. 15ECh. 4.2 - Prob. 16ECh. 4.3 - 4-17. Suppose that the cumulative distribution...Ch. 4.3 - 4-18. Suppose that the cumulative distribution...Ch. 4.3 - 4-19. Determine the cumulative distribution...Ch. 4.3 - Prob. 20ECh. 4.3 - 4-21. Determine the cumulative distribution...Ch. 4.3 - Prob. 22ECh. 4.3 - Prob. 23ECh. 4.3 - 4-24. Determine the cumulative distribution...Ch. 4.3 - 4-25. Determine the cumulative distribution...Ch. 4.3 - 4-26. The probability density function of the time...Ch. 4.3 - 4-27. The gap width is an important property of a...Ch. 4.3 - Determine the probability density function for...Ch. 4.3 - Determine the probability density function for...Ch. 4.3 - Prob. 30ECh. 4.3 - Prob. 31ECh. 4.3 - Prob. 33ECh. 4.4 - 4-35. Suppose that f(x) = 0.25 for 0 < x < 4....Ch. 4.4 - 4-36. Suppose that f(x) = 0.125x for 0 < x < 4....Ch. 4.4 - 4-37. Suppose that f(x) = 1.5x2 for −1< x < 1....Ch. 4.4 - Prob. 38ECh. 4.4 - Prob. 39ECh. 4.4 - Prob. 40ECh. 4.4 - Prob. 41ECh. 4.4 - 4.42 Determine the mean and variance of the random...Ch. 4.4 - Prob. 43ECh. 4.4 - 4-45. Suppose that contamination particle size (in...Ch. 4.4 - 4-46. Suppose that the probability density...Ch. 4.4 - 4-47. The thickness of a conductive coating in...Ch. 4.4 - 4-48. The probability density function of the...Ch. 4.4 - Prob. 49ECh. 4.5 - 4-50. Suppose that X has a continuous uniform...Ch. 4.5 - 4-51. Suppose X has a continuous uniform...Ch. 4.5 - 4-52. The net weight in pounds of a packaged...Ch. 4.5 - 4-53. The thickness of a flange on an aircraft...Ch. 4.5 - Prob. 54ECh. 4.5 - Prob. 55ECh. 4.5 - 4-56. An adult can lose or gain two pounds of...Ch. 4.5 - 4-57. A show is scheduled to start at 9:00 a.m.,...Ch. 4.5 - 4-58. The volume of a shampoo filled into a...Ch. 4.5 - 4-59. An e-mail message will arrive at a time...Ch. 4.5 - 4-60. Measurement error that is continuous and...Ch. 4.5 - 4-61. A beacon transmits a signal every 10 minutes...Ch. 4.5 - Prob. 62ECh. 4.6 - 4-63. Use Appendix Table III to determine the...Ch. 4.6 - 4-64. Use Appendix Table III to determine the...Ch. 4.6 - 4-65. Assume that Z has a standard normal...Ch. 4.6 - 4-66. Assume that Z has a standard normal...Ch. 4.6 - Prob. 67ECh. 4.6 - Prob. 68ECh. 4.6 - Prob. 69ECh. 4.6 - 4-70. Assume that X is normally distributed with a...Ch. 4.6 - 4-71. The compressive strength of samples of...Ch. 4.6 - 4-72. The time until recharge for a battery in a...Ch. 4.6 - 4-73. An article in Knee Surgery Sports Traumatol...Ch. 4.6 - 4-74. Cholesterol is a fatty substance that is an...Ch. 4.6 - Prob. 75ECh. 4.6 - 4-76. The fill volume of an automated filling...Ch. 4.6 - 4-77. In the previous exercise, suppose that the...Ch. 4.6 - 4-78. A driver’s reaction time to visual stimulus...Ch. 4.6 - 4-79. The speed of a file transfer from a server...Ch. 4.6 - 4-80. In 2002, the average height of a woman aged...Ch. 4.6 - 4-81. In an accelerator center, an experiment...Ch. 4.6 - 4-82. The demand for water use in Phoenix in 2003...Ch. 4.6 - Prob. 83ECh. 4.6 - 4-84. The diameter of the dot produced by a...Ch. 4.6 - Prob. 85ECh. 4.6 - Prob. 86ECh. 4.6 - Prob. 87ECh. 4.6 - 4-88. A study by Bechtel et al., 2009, described...Ch. 4.6 - 4-89. An article in Atmospheric Chemistry and...Ch. 4.6 - 4-90. The length of stay at a specific emergency...Ch. 4.6 - Prob. 91ECh. 4.6 - 4-92. An article in Microelectronics Reliability...Ch. 4.6 - Prob. 93ECh. 4.6 - 4-94. An article in the Journal of Cardiovascular...Ch. 4.7 - 4-95. Suppose that X is a binomial random variable...Ch. 4.7 - 4-96. Suppose that X is a Poisson random variable...Ch. 4.7 - 4-97. Suppose that X has a Poisson distribution...Ch. 4.7 - 4-98. The manufacturing of semiconductor chips...Ch. 4.7 - 4-99. There were 49.7 million people with some...Ch. 4.7 - 4-100. Phoenix water is provided to approximately...Ch. 4.7 - 4-101. An electronic office product contains 5000...Ch. 4.7 - 4-102. A corporate Web site contains errors on 50...Ch. 4.7 - 4-103. Suppose that the number of asbestos...Ch. 4.7 - 4-104. A high-volume printer produces minor...Ch. 4.7 - 4-105. Hits to a high-volume Web site are assumed...Ch. 4.7 - 4-106. An acticle in Biometrics [“Integrative...Ch. 4.7 - 4-107. An article in Atmospheric Chemistry and...Ch. 4.7 - 4-108. A set of 200 independent patients take...Ch. 4.7 - Prob. 109ECh. 4.7 - 4-110. Cabs pass your workplace according to a...Ch. 4.7 - 4-111. The number of (large) inclusions in cast...Ch. 4.8 - 4-112. Suppose that X has an exponential...Ch. 4.8 - Prob. 113ECh. 4.8 - 4-114. Suppose that X has an exponential...Ch. 4.8 - 4-115. Suppose that the counts recorded by a...Ch. 4.8 - 4-116. Suppose that the log-ons to a computer...Ch. 4.8 - 4-117. The time between calls to a plumbing supply...Ch. 4.8 - 4-118. The life of automobile voltage regulators...Ch. 4.8 - 4-119. Suppose that the time to failure (in hours)...Ch. 4.8 - 4-120. The time between the arrival of electronic...Ch. 4.8 - 4-121. The time between arrivals of taxis at a...Ch. 4.8 - Prob. 122ECh. 4.8 - 4-123. According to results from the analysis of...Ch. 4.8 - 4-124. The distance between major cracks in a...Ch. 4.8 - 4-125. The lifetime of a mechanical assembly in a...Ch. 4.8 - 4-126. The time between arrivals of small aircraft...Ch. 4.8 - Prob. 127ECh. 4.8 - Prob. 128ECh. 4.8 - Prob. 129ECh. 4.8 - Prob. 130ECh. 4.8 - Prob. 131ECh. 4.8 - Prob. 132ECh. 4.8 - Prob. 133ECh. 4.8 - 4-134. Requests for service in a queuing model...Ch. 4.8 - 4-135. An article in Vaccine [“Modeling the...Ch. 4.8 - 4-136. An article in Ad Hoc Networks [“Underwater...Ch. 4.9 - 4-137. Use the properties of the gamma function to...Ch. 4.9 - Prob. 138ECh. 4.9 - 4-139. Calls to a telephone system follow a...Ch. 4.9 - Prob. 140ECh. 4.9 - Prob. 141ECh. 4.9 - Prob. 142ECh. 4.9 - Prob. 143ECh. 4.9 - Prob. 144ECh. 4.9 - Prob. 145ECh. 4.9 - Prob. 146ECh. 4.9 - Prob. 147ECh. 4.9 - 4-148. Use the result for the gamma distribution...Ch. 4.9 - Prob. 149ECh. 4.9 - 4-150. The total service time of a multistep...Ch. 4.9 - Prob. 151ECh. 4.9 - 4-152. An article in Mathematical Biosciences...Ch. 4.10 - Prob. 153ECh. 4.10 - Prob. 154ECh. 4.10 - Prob. 155ECh. 4.10 - Prob. 156ECh. 4.10 - Prob. 157ECh. 4.10 - 4-158. Assume that the life of a packaged magnetic...Ch. 4.10 - Prob. 159ECh. 4.10 - Prob. 160ECh. 4.10 - Prob. 162ECh. 4.10 - Prob. 163ECh. 4.10 - Prob. 164ECh. 4.10 - Prob. 165ECh. 4.10 - Prob. 167ECh. 4.10 - Prob. 168ECh. 4.10 - Prob. 169ECh. 4.11 - 4-170. Suppose that X has a lognormal distribution...Ch. 4.11 - Prob. 171ECh. 4.11 - 4-172. Suppose that X has a lognormal distribution...Ch. 4.11 - 4-173. The length of time (in seconds) that a user...Ch. 4.11 - 4-174. Suppose that X has a lognormal distribution...Ch. 4.11 - 4-175. The lifetime of a semiconductor laser has a...Ch. 4.11 - Prob. 176ECh. 4.11 - Prob. 177ECh. 4.11 - Prob. 178ECh. 4.11 - Prob. 179ECh. 4.11 - Prob. 180ECh. 4.11 - Prob. 181ECh. 4.11 - Prob. 182ECh. 4.11 - Prob. 183ECh. 4.12 - Prob. 184ECh. 4.12 - Prob. 185ECh. 4.12 - Prob. 186ECh. 4.12 - Prob. 187ECh. 4.12 - Prob. 188ECh. 4.12 - Prob. 189ECh. 4.12 - Prob. 190ECh. 4.12 - Prob. 191ECh. 4 - Prob. 192SECh. 4 - Prob. 193SECh. 4 - Prob. 194SECh. 4 - 4-195. + The length of an injection-molded plastic...Ch. 4 - 4-196. + The sick-leave time of employees in a...Ch. 4 - Prob. 197SECh. 4 - Prob. 198SECh. 4 - 4-199. + When a bus service reduces fares, a...Ch. 4 - Prob. 200SECh. 4 - Prob. 201SECh. 4 - Prob. 202SECh. 4 - Prob. 203SECh. 4 - Prob. 204SECh. 4 - 4-205. + The CPU of a personal computer has a...Ch. 4 - Prob. 206SECh. 4 - Prob. 207SECh. 4 - Prob. 208SECh. 4 - 4-209. + Without an automated irrigation system,...Ch. 4 - 4-210. With an automated irrigation system, a...Ch. 4 - Prob. 211SECh. 4 - Prob. 212SECh. 4 - Prob. 213SECh. 4 - Prob. 214SECh. 4 - Prob. 215SECh. 4 - Prob. 216SECh. 4 - 4-217. + A square inch of carpeting contains 50...Ch. 4 - Prob. 218SECh. 4 - Prob. 219SECh. 4 - 4-221. Consider the regional right ventricle...Ch. 4 - Prob. 222SECh. 4 - Prob. 223SECh. 4 - Prob. 224SECh. 4 - Prob. 225SECh. 4 - Prob. 226SECh. 4 - Prob. 227SECh. 4 - Prob. 228SECh. 4 - Prob. 229SECh. 4 - Prob. 230SECh. 4 - Prob. 231SECh. 4 - Prob. 232SECh. 4 - Prob. 233SECh. 4 - 4-234. A process is said to be of six-sigma...
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- 2. [20] Let {X1,..., Xn} be a random sample from Ber(p), where p = (0, 1). Consider two estimators of the parameter p: 1 p=X_and_p= n+2 (x+1). For each of p and p, find the bias and MSE.arrow_forward1. [20] The joint PDF of RVs X and Y is given by xe-(z+y), r>0, y > 0, fx,y(x, y) = 0, otherwise. (a) Find P(0X≤1, 1arrow_forward4. [20] Let {X1,..., X} be a random sample from a continuous distribution with PDF f(x; 0) = { Axe 5 0, x > 0, otherwise. where > 0 is an unknown parameter. Let {x1,...,xn} be an observed sample. (a) Find the value of c in the PDF. (b) Find the likelihood function of 0. (c) Find the MLE, Ô, of 0. (d) Find the bias and MSE of 0.arrow_forward3. [20] Let {X1,..., Xn} be a random sample from a binomial distribution Bin(30, p), where p (0, 1) is unknown. Let {x1,...,xn} be an observed sample. (a) Find the likelihood function of p. (b) Find the MLE, p, of p. (c) Find the bias and MSE of p.arrow_forwardGiven the sample space: ΩΞ = {a,b,c,d,e,f} and events: {a,b,e,f} A = {a, b, c, d}, B = {c, d, e, f}, and C = {a, b, e, f} For parts a-c: determine the outcomes in each of the provided sets. Use proper set notation. a. (ACB) C (AN (BUC) C) U (AN (BUC)) AC UBC UCC b. C. d. If the outcomes in 2 are equally likely, calculate P(AN BNC).arrow_forwardSuppose a sample of O-rings was obtained and the wall thickness (in inches) of each was recorded. Use a normal probability plot to assess whether the sample data could have come from a population that is normally distributed. Click here to view the table of critical values for normal probability plots. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. 0.191 0.186 0.201 0.2005 0.203 0.210 0.234 0.248 0.260 0.273 0.281 0.290 0.305 0.310 0.308 0.311 Using the correlation coefficient of the normal probability plot, is it reasonable to conclude that the population is normally distributed? Select the correct choice below and fill in the answer boxes within your choice. (Round to three decimal places as needed.) ○ A. Yes. The correlation between the expected z-scores and the observed data, , exceeds the critical value, . Therefore, it is reasonable to conclude that the data come from a normal population. ○…arrow_forwardding question ypothesis at a=0.01 and at a = 37. Consider the following hypotheses: 20 Ho: μ=12 HA: μ12 Find the p-value for this hypothesis test based on the following sample information. a. x=11; s= 3.2; n = 36 b. x = 13; s=3.2; n = 36 C. c. d. x = 11; s= 2.8; n=36 x = 11; s= 2.8; n = 49arrow_forward13. A pharmaceutical company has developed a new drug for depression. There is a concern, however, that the drug also raises the blood pressure of its users. A researcher wants to conduct a test to validate this claim. Would the manager of the pharmaceutical company be more concerned about a Type I error or a Type II error? Explain.arrow_forwardFind the z score that corresponds to the given area 30% below z.arrow_forwardFind the following probability P(z<-.24)arrow_forward3. Explain why the following statements are not correct. a. "With my methodological approach, I can reduce the Type I error with the given sample information without changing the Type II error." b. "I have already decided how much of the Type I error I am going to allow. A bigger sample will not change either the Type I or Type II error." C. "I can reduce the Type II error by making it difficult to reject the null hypothesis." d. "By making it easy to reject the null hypothesis, I am reducing the Type I error."arrow_forwardGiven the following sample data values: 7, 12, 15, 9, 15, 13, 12, 10, 18,12 Find the following: a) Σ x= b) x² = c) x = n d) Median = e) Midrange x = (Enter a whole number) (Enter a whole number) (use one decimal place accuracy) (use one decimal place accuracy) (use one decimal place accuracy) f) the range= g) the variance, s² (Enter a whole number) f) Standard Deviation, s = (use one decimal place accuracy) Use the formula s² ·Σx² -(x)² n(n-1) nΣ x²-(x)² 2 Use the formula s = n(n-1) (use one decimal place accuracy)arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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