a. Explanation Given info: The probability of cracking an egg is 1%. Assume that each egg loads is an independent event . A customer will complain if there are more than one egg per dozen is cracked. Calculation: The random variable X denotes that number of eggs that are cracked. Criteria for binomial distribution: Each experiment has fixed number of trials Each trial is independent of the other There are two possible outcomes. They are success and failure. Probability of success is same for all trials. Here, the number of trials ( n = 12 ) is fixed. Hence the first condition is satisfied. The trials are independent. Hence, the second condition is satisfied. There are two outcomes, the eggs that are cracked (success) or eggs that are not cracked (failure). Hence, the third condition is satisfied. P ( egg cracked ) = 1 % = 0.01 That is, P ( Success ) = 0.01 . There is a fixed probability that eggs that are cracked. Hence, the fourth condition is also satisfied. Thus, it is a binomial experiment. Therefore, X follow binomial distribution with parameters n = 12 and p = 0.01 . The probability of obtaining X successes in n independent trails of a binomial experiment is, f ( x ) = P ( X = x ) = ( n x ) p x ( b. To determine Compute the probability that a carton of a dozen eggs results in a complaint. c. To determine Compute the mean and standard deviation of the number of cracked eggs in the carton of a dozen eggs.

Applied Statistics and Probability for Engineers

6th Edition

ISBN: 9781118802250

Author: Montgomery

Publisher: WILEY

See similar textbooks

Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Videos

Question

Chapter 3, Problem 178SE

To determine

Compute the distribution of cracked eggs per dozen and include the parameters.

To determine

Compute the probability that a carton of a dozen eggs results in a complaint.

To determine

Compute the mean and standard deviation of the number of cracked eggs in the carton of a dozen eggs.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 3, Problem 177SE

Chapter 3, Problem 179SE

Students have asked these similar questions

Suppose you are gambling on a roulette wheel. Each time the wheel is spun, the result is one of the outcomes 0, 1, and so on through 36. Of these outcomes, 18 are red, 18 are black, and 1 is green. On each spin you bet $5 that a red outcome will occur and $1 that the green outcome will occur. If red occurs, you win a net $4. (You win $10 from red and nothing from green.) If green occurs, you win a net $24. (You win $30 from green and nothing from red.) If black occurs, you lose everything you bet for a loss of $6. a. Use simulation to generate 1,000 plays from this strategy. Each play should indicate the net amount won or lost. Then, based on these outcomes, calculate a 95% confidence interval for the total net amount won or lost from 1,000 plays of the game. (Round your answers to two decimal places and if your answer is negative value, enter "minus" sign.) I worked out the Upper Limit, but I can't seem to arrive at the correct answer for the Lower Limit. What is the Lower Limit?…

Let us suppose we have some article reported on a study of potential sources of injury to equine veterinarians conducted at a university veterinary hospital. Forces on the hand were measured for several common activities that veterinarians engage in when examining or treating horses. We will consider the forces on the hands for two tasks, lifting and using ultrasound. Assume that both sample sizes are 6, the sample mean force for lifting was 6.2 pounds with standard deviation 1.5 pounds, and the sample mean force for using ultrasound was 6.4 pounds with standard deviation 0.3 pounds. Assume that the standard deviations are known. Suppose that you wanted to detect a true difference in mean force of 0.25 pounds on the hands for these two activities. Under the null hypothesis, 40 0. What level of type II error would you recommend here? = Round your answer to four decimal places (e.g. 98.7654). Use α = 0.05. β = 0.0594 What sample size would be required? Assume the sample sizes are to be…

Consider the hypothesis test Ho: 0 s² = = 4.5; s² = 2.3. Use a = 0.01. = σ against H₁: 6 > σ2. Suppose that the sample sizes are n₁ = 20 and 2 = 8, and that (a) Test the hypothesis. Round your answers to two decimal places (e.g. 98.76). The test statistic is fo = 1.96 The critical value is f = 6.18 Conclusion: fail to reject the null hypothesis at a = 0.01. (b) Construct the confidence interval on 02/2/622 which can be used to test the hypothesis: (Round your answer to two decimal places (e.g. 98.76).) 035

Chapter 3 Solutions

Applied Statistics and Probability for Engineers

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. 24E Ch. 3.2 - Prob. 25E Ch. 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. 43E Ch. 3.3 - Prob. 44E Ch. 3.3 - 3-45. Determine the cumulative distribution...Ch. 3.3 - Prob. 46E Ch. 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. 62E Ch. 3.4 - 3-63. Determine the mean and variance of the...Ch. 3.4 - Prob. 64E Ch. 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. 79E Ch. 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. 99E Ch. 3.6 - Prob. 100E Ch. 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. 105E Ch. 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. 120E Ch. 3.7 - 3-121. Consider a sequence of independent...Ch. 3.7 - Prob. 122E Ch. 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. 132E Ch. 3.7 - Prob. 133E Ch. 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. 136E Ch. 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. 139E Ch. 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. 142E Ch. 3.8 - Prob. 143E Ch. 3.8 - Prob. 144E Ch. 3.8 - 3-145. A research study uses 800 men under the age...Ch. 3.8 - Prob. 146E Ch. 3.8 - Prob. 147E Ch. 3.8 - 3-148. A state runs a lottery in which six numbers...Ch. 3.8 - Prob. 149E Ch. 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. 155E Ch. 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. 158E Ch. 3.9 - Prob. 159E Ch. 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. 163E Ch. 3.9 - 3-164. The number of flaws in bolts of cloth in...Ch. 3.9 - Prob. 165E Ch. 3.9 - 3-166. The number of cracks in a section of...Ch. 3.9 - Prob. 167E Ch. 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. 171E Ch. 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. 175SE Ch. 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. 178SE Ch. 3 - 3-179. A total of 12 cells are replicated. Freshly...Ch. 3 - Prob. 180SE Ch. 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. 183SE Ch. 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. 187SE Ch. 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. 191SE Ch. 3 - 3-192. The number of errors in a textbook follows...Ch. 3 - Prob. 193SE Ch. 3 - Prob. 194SE Ch. 3 - 3-195. In a manufacturing process that laminates...Ch. 3 - Prob. 196SE Ch. 3 - Prob. 197SE Ch. 3 - 3-198. A manufacturer of a consumer electronics...Ch. 3 - Prob. 199SE Ch. 3 - 3-200. The random variable X has the following...Ch. 3 - Prob. 201SE Ch. 3 - Prob. 202SE Ch. 3 - Prob. 203SE Ch. 3 - 3-204. An installation technician for a...Ch. 3 - Prob. 205SE Ch. 3 - Prob. 206SE Ch. 3 - 3-207. Messages arrive to a computer server...Ch. 3 - 3-208. Flaws occur in the interior of plastic used...Ch. 3 - Prob. 209SE Ch. 3 - Prob. 210SE Ch. 3 - Prob. 211SE Ch. 3 - Prob. 212SE Ch. 3 - Prob. 213SE Ch. 3 - Prob. 214SE Ch. 3 - Prob. 215SE Ch. 3 - Prob. 216SE Ch. 3 - Prob. 217SE Ch. 3 - Prob. 218SE Ch. 3 - Prob. 219SE

Knowledge Booster

$Statistics$

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.