Applied Statistics and Probability for Engineers
6th Edition
ISBN: 9781118539712
Author: Douglas C. Montgomery
Publisher: WILEY
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Question
Chapter 3.3, Problem 53E
To determine
Compute the cumulative distribution
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
1. A consumer group claims that the mean annual consumption of cheddar cheese by a person in
the United States is at most 10.3 pounds. A random sample of 100 people in the United States has
a mean annual cheddar cheese consumption of 9.9 pounds. Assume the population standard
deviation is 2.1 pounds. At a = 0.05, can you reject the claim? (Adapted from U.S. Department of
Agriculture)
State the hypotheses:
Calculate the test statistic:
Calculate the P-value:
Conclusion (reject or fail to reject Ho):
2. The CEO of a manufacturing facility claims that the mean workday of the company's assembly
line employees is less than 8.5 hours. A random sample of 25 of the company's assembly line
employees has a mean workday of 8.2 hours. Assume the population standard deviation is 0.5
hour and the population is normally distributed. At a = 0.01, test the CEO's claim.
State the hypotheses:
Calculate the test statistic:
Calculate the P-value:
Conclusion (reject or fail to reject Ho):
Statistics
21.
find the mean.
and
variance of the
following:
Ⓒ x(t) = Ut +V, and V indepriv. s.t
U.VN NL0, 63).
X(t) = t² + Ut +V, U and V incepires have N (0,8)
Ut
①xt = e UNN (0162)
~ X+ = UCOSTE, UNNL0, 62)
SU, Oct
⑤Xt=
7
where U. Vindp.rus
+> ½
have NL, 62).
⑥Xn = ΣY, 41, 42, 43, ... Yn vandom sample
K=1
Text
with mean zen and variance 6
A psychology researcher conducted a Chi-Square Test of Independence to examine whether there is a relationship between college students’ year in school (Freshman, Sophomore, Junior, Senior) and their preferred coping strategy for academic stress (Problem-Focused, Emotion-Focused, Avoidance). The test yielded the following result:
image.png
Interpret the results of this analysis. In your response, clearly explain:
Whether the result is statistically significant and why.
What this means about the relationship between year in school and coping strategy.
What the researcher should conclude based on these findings.
Chapter 3 Solutions
Applied Statistics and Probability for Engineers
Ch. 3.1 - Prob. 1ECh. 3.1 - For each of the following exercises, determine the...Ch. 3.1 - For each of the following exercises, determine the...Ch. 3.1 - For each of the following exercises, determine the...Ch. 3.1 - For each of the following exercises, determine the...Ch. 3.1 - For each of the following exercises, determine the...Ch. 3.1 - Prob. 7ECh. 3.1 - For each of the following exercises, determine the...Ch. 3.1 - For each of the following exercises, determine the...Ch. 3.1 - For each of the following exercises, determine the...
Ch. 3.1 - For each of the following exercises, determine the...Ch. 3.1 - For each of the following exercises, determine the...Ch. 3.1 - For each of the following exercises, determine the...Ch. 3.1 - For each of the following exercises, determine the...Ch. 3.1 - For each of the following exercises, determine the...Ch. 3.2 - 3-16. The sample space of a random experiment is...Ch. 3.2 - For Exercises 3-17 to 3-21, verify that the...Ch. 3.2 - For Exercises 3-17 to 3-21, verify that the...Ch. 3.2 - For Exercises 3-17 to 3-21, verify that the...Ch. 3.2 - For Exercises 3-17 to 3-21, verify that the...Ch. 3.2 - For Exercises 3-17 to 3-21, verify that the...Ch. 3.2 - 3-22. Consider the hospital patients in Example...Ch. 3.2 - 3-23. An article in Knee Surgery, Sports...Ch. 3.2 - Prob. 24ECh. 3.2 - Prob. 25ECh. 3.2 - 3-26. The space shuttle flight control system...Ch. 3.2 - 3-27. A disk drive manufacturer sells storage...Ch. 3.2 - 3-28. Marketing estimates that a new instrument...Ch. 3.2 - 3-29. The distributor of a machine for cytogenics...Ch. 3.2 - 3-30. An assembly consists of two mechanical...Ch. 3.2 - 3-31. An assembly consists of three mechanical...Ch. 3.2 - 3-32. The data from 200 endothermic reactions...Ch. 3.2 - 3-33. Actual lengths of stay at a hospital’s...Ch. 3.2 - 3-34. The distribution of the time until a Web...Ch. 3.2 - 3-35 The following table shows the typical depth...Ch. 3.2 - 3-36. Consider the wafers with contamination...Ch. 3.2 - 3-37. Consider the circuit in Example 2-32. Assume...Ch. 3.3 - 3-38. Determine the cumulative distribution...Ch. 3.3 - 3-39. Determine the cumulative distribution...Ch. 3.3 - 3-40. Determine the cumulative distribution...Ch. 3.3 - 3-41. Determine the cumulative distribution...Ch. 3.3 - 3-42. Determine the cumulative distribution...Ch. 3.3 - Prob. 43ECh. 3.3 - Prob. 44ECh. 3.3 - 3-45. Determine the cumulative distribution...Ch. 3.3 - Prob. 46ECh. 3.3 - 3-47. Determine the cumulative distribution...Ch. 3.3 - 3-48. Determine the cumulative distribution...Ch. 3.3 - Verify that the following functions are cumulative...Ch. 3.3 - Verify that the following functions are cumulative...Ch. 3.3 - Verify that the following functions are cumulative...Ch. 3.3 - Verify that the following functions are cumulative...Ch. 3.3 - 3-53. Determine the cumulative distribution...Ch. 3.3 - 3-54. Determine the cumulative distribution...Ch. 3.3 - 3-55. Determine the cumulative distribution...Ch. 3.3 - 3-56. Determine the cumulative distribution...Ch. 3.4 - 3-57. If the range of X is the set {0,1,2,3,4} and...Ch. 3.4 - 3-58. Determine the mean and variance of the...Ch. 3.4 - 3-59. Determine the mean and variance of the...Ch. 3.4 - 3-60. Determine the mean and variance of the...Ch. 3.4 - 3-61. Determine the mean and variance of the...Ch. 3.4 - Prob. 62ECh. 3.4 - 3-63. Determine the mean and variance of the...Ch. 3.4 - Prob. 64ECh. 3.4 - 3-65. The range of the random variable X is [0, 1,...Ch. 3.4 - 3-66. In a NiCd battery, a fully charged cell is...Ch. 3.4 - 3-67. The space shuttle flight control system...Ch. 3.4 - 3-68. Trees are subjected to different levels of...Ch. 3.4 - 3-69. An article in the Journal of Database...Ch. 3.4 - 3-70. Calculate the mean and variance for the...Ch. 3.4 - 3-71. Calculate the mean and variance for the...Ch. 3.4 - 3-72. Calculate the mean and variance for the...Ch. 3.4 - 3-73. Calculate the mean and variance for the...Ch. 3.4 - 3-74. Calculate the mean and variance for the...Ch. 3.4 - 3-75. Calculate the mean for the random variable...Ch. 3.5 - 3-76. Let the random variable X have a discrete...Ch. 3.5 - 3-77. Let the random variable X have a discrete...Ch. 3.5 - 3-78. Thickness measurements of a coating process...Ch. 3.5 - Prob. 79ECh. 3.5 - 3-80. The lengths of plate glass parts are...Ch. 3.5 - 3-81. Assume that the wavelengths of...Ch. 3.5 - 3-82. The probability of an operator entering...Ch. 3.5 - 3-83. Suppose that X has a discrete uniform...Ch. 3.5 - 3-84. Show that for a discrete uniform random...Ch. 3.5 - 3-85. The number of pages in a PDF document you...Ch. 3.5 - 3-86. Suppose that nine-digit Social Security...Ch. 3.5 - 3-87. Suppose that 1000 seven-digit telephone...Ch. 3.5 - 3-88. The probability that data are entered...Ch. 3.5 - 3-89. Each multiple-choice question on an exam has...Ch. 3.5 - 3-90. Consider the hospital data in Example 2-8....Ch. 3.6 - 3-91. For each scenario (a)–(j), state whether or...Ch. 3.6 - 3-92. Let X be a binomial random variable with p =...Ch. 3.6 - 3-93. Let X be a binomial random variable with p =...Ch. 3.6 - 3-94. The random variable X has a binomial...Ch. 3.6 - 3-95. The random variable X has a binomial...Ch. 3.6 - 3-96. The random variable X has a binomial...Ch. 3.6 - 3-97. Sketch the probability mass function of a...Ch. 3.6 - 3-98. Determine the cumulative distribution...Ch. 3.6 - Prob. 99ECh. 3.6 - Prob. 100ECh. 3.6 - 3-101. The phone lines to an airline reservation...Ch. 3.6 - 3-102. A multiple-choice test contains 25...Ch. 3.6 - 3-103. A particularly long traffic light on your...Ch. 3.6 - 3-104. Samples of rejuvenated mitochondria are...Ch. 3.6 - Prob. 105ECh. 3.6 - 3-106. Heart failure is due to either natural...Ch. 3.6 - 3-107. A computer system uses passwords that are...Ch. 3.6 - 3-108. Samples of 20 parts from a metal punching...Ch. 3.6 - 3-109. Because all airline passengers do not show...Ch. 3.6 - 3-110. This exercise illustrates that poor quality...Ch. 3.6 - 3-111. Consider the lengths of stay at a...Ch. 3.6 - 3-112. Consider the patient data in Example 2-8....Ch. 3.6 - 3-113. Assume that a Web site changes its content...Ch. 3.6 - 3-114. Consider the endothermic reactions in...Ch. 3.6 - 3-115. The probability that a visitor to a Web...Ch. 3.6 - 3-116. Consider the circuit in Example 2-34....Ch. 3.6 - 3-117. Consider the time to recharge the flash in...Ch. 3.6 - 3-118. Consider the patient data in Example 2-8....Ch. 3.7 - 3-119. Suppose that the random variable X has a...Ch. 3.7 - Prob. 120ECh. 3.7 - 3-121. Consider a sequence of independent...Ch. 3.7 - Prob. 122ECh. 3.7 - 3-123. The probability of a successful optical...Ch. 3.7 - 3-124. In a clinical study, volunteers are tested...Ch. 3.7 - 3-125. Assume that each of your calls to a popular...Ch. 3.7 - 3-126. A player of a video game is confronted with...Ch. 3.7 - 3-127. Heart failure is due to either natural...Ch. 3.7 - 3-128. A computer system uses passwords...Ch. 3.7 - 3-129. A trading company uses eight computers to...Ch. 3.7 - 3-130. Assume that 20 parts are checked each hour...Ch. 3.7 - 3-131. A fault-tolerant system that processes...Ch. 3.7 - Prob. 132ECh. 3.7 - Prob. 133ECh. 3.7 - 3-134. Consider the endothermic reactions in...Ch. 3.7 - 3-135. A Web site randomly selects among 10...Ch. 3.7 - Prob. 136ECh. 3.7 - 3-137. Consider the time to recharge the flash in...Ch. 3.7 - 3-138. An array of 30 LED bulbs is used in an...Ch. 3.7 - Prob. 139ECh. 3.7 - 3-140. Customers visit a Web site, and the...Ch. 3.8 - 3-141. Suppose that X has a hypergeometric...Ch. 3.8 - Prob. 142ECh. 3.8 - Prob. 143ECh. 3.8 - Prob. 144ECh. 3.8 - 3-145. A research study uses 800 men under the age...Ch. 3.8 - Prob. 146ECh. 3.8 - Prob. 147ECh. 3.8 - 3-148. A state runs a lottery in which six numbers...Ch. 3.8 - Prob. 149ECh. 3.8 - 3-150. Calculate the finite population...Ch. 3.8 - 3-151. Consider the visits that result in leave...Ch. 3.8 - 3-152. Consider the nonfailed wells in Exercises...Ch. 3.8 - 3-153. Consider the semiconductor wafer data in...Ch. 3.8 - 3-154. Suppose that a healthcare provider selects...Ch. 3.8 - Prob. 155ECh. 3.8 - 3-156. A utility company might offer electrical...Ch. 3.9 - 3-157. Suppose that X has a Poisson distribution...Ch. 3.9 - Prob. 158ECh. 3.9 - Prob. 159ECh. 3.9 - 3-160. The number of telephone calls that arrive...Ch. 3.9 - 3-161. Astronomers treat the number of stars in a...Ch. 3.9 - 3-162. Data from www.centralhudsonlabs.com...Ch. 3.9 - Prob. 163ECh. 3.9 - 3-164. The number of flaws in bolts of cloth in...Ch. 3.9 - Prob. 165ECh. 3.9 - 3-166. The number of cracks in a section of...Ch. 3.9 - Prob. 167ECh. 3.9 - 3-168. The number of failures of a testing...Ch. 3.9 - 3-169. The number of content changes to a Web site...Ch. 3.9 - 3-170. The number of views of a page on a Web site...Ch. 3.9 - Prob. 171ECh. 3.9 - 3-172. Orders arrive at a Web site according to a...Ch. 3.9 - 3-173. The article “An Association Between Fine...Ch. 3.9 - 3-174. Inclusions are defects in poured metal...Ch. 3 - Prob. 175SECh. 3 - 3-176. Let X denote the number of bits received in...Ch. 3 - 3-177. Batches that consist of 50 coil springs...Ch. 3 - Prob. 178SECh. 3 - 3-179. A total of 12 cells are replicated. Freshly...Ch. 3 - Prob. 180SECh. 3 - 3-181. A particularly long traffic light on your...Ch. 3 - 3-182. The probability is 0.6 that a calibration...Ch. 3 - Prob. 183SECh. 3 - 3-184. The probability that an eagle kills a...Ch. 3 - 3-185. Traffic flow is traditionally modeled as a...Ch. 3 - 3-186. A shipment of chemicals arrives in 15...Ch. 3 - Prob. 187SECh. 3 - 3-188. The probability that your call to a service...Ch. 3 - 3-189. The probability that your call to a service...Ch. 3 - 3-190. The number of messages that arrive at a Web...Ch. 3 - Prob. 191SECh. 3 - 3-192. The number of errors in a textbook follows...Ch. 3 - Prob. 193SECh. 3 - Prob. 194SECh. 3 - 3-195. In a manufacturing process that laminates...Ch. 3 - Prob. 196SECh. 3 - Prob. 197SECh. 3 - 3-198. A manufacturer of a consumer electronics...Ch. 3 - Prob. 199SECh. 3 - 3-200. The random variable X has the following...Ch. 3 - Prob. 201SECh. 3 - Prob. 202SECh. 3 - Prob. 203SECh. 3 - 3-204. An installation technician for a...Ch. 3 - Prob. 205SECh. 3 - Prob. 206SECh. 3 - 3-207. Messages arrive to a computer server...Ch. 3 - 3-208. Flaws occur in the interior of plastic used...Ch. 3 - Prob. 209SECh. 3 - Prob. 210SECh. 3 - Prob. 211SECh. 3 - Prob. 212SECh. 3 - Prob. 213SECh. 3 - Prob. 214SECh. 3 - Prob. 215SECh. 3 - Prob. 216SECh. 3 - Prob. 217SECh. 3 - Prob. 218SECh. 3 - Prob. 219SE
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Similar questions
- A school counselor is conducting a research study to examine whether there is a relationship between the number of times teenagers report vaping per week and their academic performance, measured by GPA. The counselor collects data from a sample of high school students. Write the null and alternative hypotheses for this study. Clearly state your hypotheses in terms of the correlation between vaping frequency and academic performance. EditViewInsertFormatToolsTable 12pt Paragrapharrow_forwardA smallish urn contains 25 small plastic bunnies – 7 of which are pink and 18 of which are white. 10 bunnies are drawn from the urn at random with replacement, and X is the number of pink bunnies that are drawn. (a) P(X = 5) ≈ (b) P(X<6) ≈ The Whoville small urn contains 100 marbles – 60 blue and 40 orange. The Grinch sneaks in one night and grabs a simple random sample (without replacement) of 15 marbles. (a) The probability that the Grinch gets exactly 6 blue marbles is [ Select ] ["≈ 0.054", "≈ 0.043", "≈ 0.061"] . (b) The probability that the Grinch gets at least 7 blue marbles is [ Select ] ["≈ 0.922", "≈ 0.905", "≈ 0.893"] . (c) The probability that the Grinch gets between 8 and 12 blue marbles (inclusive) is [ Select ] ["≈ 0.801", "≈ 0.760", "≈ 0.786"] . The Whoville small urn contains 100 marbles – 60 blue and 40 orange. The Grinch sneaks in one night and grabs a simple random sample (without replacement) of 15 marbles. (a)…arrow_forwardSuppose an experiment was conducted to compare the mileage(km) per litre obtained by competing brands of petrol I,II,III. Three new Mazda, three new Toyota and three new Nissan cars were available for experimentation. During the experiment the cars would operate under same conditions in order to eliminate the effect of external variables on the distance travelled per litre on the assigned brand of petrol. The data is given as below: Brands of Petrol Mazda Toyota Nissan I 10.6 12.0 11.0 II 9.0 15.0 12.0 III 12.0 17.4 13.0 (a) Test at the 5% level of significance whether there are signi cant differences among the brands of fuels and also among the cars. [10] (b) Compute the standard error for comparing any two fuel brands means. Hence compare, at the 5% level of significance, each of fuel brands II, and III with the standard fuel brand I. [10]arrow_forward
- Analyze the residuals of a linear regression model and select the best response. yes, the residual plot does not show a curve no, the residual plot shows a curve yes, the residual plot shows a curve no, the residual plot does not show a curve I answered, "No, the residual plot shows a curve." (and this was incorrect). I am not sure why I keep getting these wrong when the answer seems obvious. Please help me understand what the yes and no references in the answer.arrow_forwarda. Find the value of A.b. Find pX(x) and py(y).c. Find pX|y(x|y) and py|X(y|x)d. Are x and y independent? Why or why not?arrow_forwardAnalyze the residuals of a linear regression model and select the best response.Criteria is simple evaluation of possible indications of an exponential model vs. linear model) no, the residual plot does not show a curve yes, the residual plot does not show a curve yes, the residual plot shows a curve no, the residual plot shows a curve I selected: yes, the residual plot shows a curve and it is INCORRECT. Can u help me understand why?arrow_forward
- You have been hired as an intern to run analyses on the data and report the results back to Sarah; the five questions that Sarah needs you to address are given below. please do it step by step on excel Does there appear to be a positive or negative relationship between price and screen size? Use a scatter plot to examine the relationship. Determine and interpret the correlation coefficient between the two variables. In your interpretation, discuss the direction of the relationship (positive, negative, or zero relationship). Also discuss the strength of the relationship. Estimate the relationship between screen size and price using a simple linear regression model and interpret the estimated coefficients. (In your interpretation, tell the dollar amount by which price will change for each unit of increase in screen size). Include the manufacturer dummy variable (Samsung=1, 0 otherwise) and estimate the relationship between screen size, price and manufacturer dummy as a multiple…arrow_forwardHere is data with as the response variable. x y54.4 19.124.9 99.334.5 9.476.6 0.359.4 4.554.4 0.139.2 56.354 15.773.8 9-156.1 319.2Make a scatter plot of this data. Which point is an outlier? Enter as an ordered pair, e.g., (x,y). (x,y)= Find the regression equation for the data set without the outlier. Enter the equation of the form mx+b rounded to three decimal places. y_wo= Find the regression equation for the data set with the outlier. Enter the equation of the form mx+b rounded to three decimal places. y_w=arrow_forwardYou have been hired as an intern to run analyses on the data and report the results back to Sarah; the five questions that Sarah needs you to address are given below. please do it step by step Does there appear to be a positive or negative relationship between price and screen size? Use a scatter plot to examine the relationship. Determine and interpret the correlation coefficient between the two variables. In your interpretation, discuss the direction of the relationship (positive, negative, or zero relationship). Also discuss the strength of the relationship. Estimate the relationship between screen size and price using a simple linear regression model and interpret the estimated coefficients. (In your interpretation, tell the dollar amount by which price will change for each unit of increase in screen size). Include the manufacturer dummy variable (Samsung=1, 0 otherwise) and estimate the relationship between screen size, price and manufacturer dummy as a multiple linear…arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
Probability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage Learning
Statistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSON
The Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. Freeman
Introduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman
MATLAB: An Introduction with Applications
Statistics
ISBN:9781119256830
Author:Amos Gilat
Publisher:John Wiley & Sons Inc
Probability and Statistics for Engineering and th...
Statistics
ISBN:9781305251809
Author:Jay L. Devore
Publisher:Cengage Learning
Statistics for The Behavioral Sciences (MindTap C...
Statistics
ISBN:9781305504912
Author:Frederick J Gravetter, Larry B. Wallnau
Publisher:Cengage Learning
Elementary Statistics: Picturing the World (7th E...
Statistics
ISBN:9780134683416
Author:Ron Larson, Betsy Farber
Publisher:PEARSON
The Basic Practice of Statistics
Statistics
ISBN:9781319042578
Author:David S. Moore, William I. Notz, Michael A. Fligner
Publisher:W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:9781319013387
Author:David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:W. H. Freeman
Continuous Probability Distributions - Basic Introduction; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=QxqxdQ_g2uw;License: Standard YouTube License, CC-BY
Probability Density Function (p.d.f.) Finding k (Part 1) | ExamSolutions; Author: ExamSolutions;https://www.youtube.com/watch?v=RsuS2ehsTDM;License: Standard YouTube License, CC-BY
Find the value of k so that the Function is a Probability Density Function; Author: The Math Sorcerer;https://www.youtube.com/watch?v=QqoCZWrVnbA;License: Standard Youtube License