Applied Statistics and Probability for Engineers
6th Edition
ISBN: 9781118539712
Author: Douglas C. Montgomery
Publisher: WILEY
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Chapter 4.3, Problem 33E
To determine
Find the cumulative distribution
Calculate the value of
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The mean height of women in a country (ages 20-29) is 63.7 inches. A random sample of 65 women in this age group
is selected. What is the probability that the mean height for the sample is greater than 64 inches? Assume σ = 2.68.
The probability that the mean height for the sample is greater than 64 inches is
(Round to four decimal places as needed.)
In a survey of a group of men, the heights in the 20-29 age group were normally distributed, with a mean of 69.6 inches
and a standard deviation of 4.0 inches. A study participant is randomly selected. Complete parts (a) through (d) below.
(a) Find the probability that a study participant has a height that is less than 68 inches.
The probability that the study participant selected at random is less than 68 inches tall is 0.4. (Round to four decimal
places as needed.)
20
2
PEER REPLY 1:
Choose a classmate's Main Post and review their decision making process.
1. Choose a risk level for each of the states of nature (assign a probability
value to each).
2. Explain why each risk level is chosen.
3. Which alternative do you believe would be the best based on the maximum
EMV?
4. Do you feel determining the expected value with perfect information
(EVWPI) is worthwhile in this situation? Why or why not?
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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