Concept explainers
Suppose that the space shuttle has three separate computer control systems: the main system and two backup duplicates of it. The first backup would monitor the main system and kick in if the main system failed. Similarly, the second backup would monitor the first. We can assume that the failure of one system is independent of the failure of another system, since the systems are separate. The probability of failure for any one system on any one mission is known to be 0.01.
a. Find the probability that the shuttle is left with no computer control system on a mission.
b. How many backup systems does the space shuttle need if the probability that the shuttle is left with no computer control system on a mission must be
Want to see the full answer?
Check out a sample textbook solutionChapter 3 Solutions
EBK MATHEMATICS: A PRACTICAL ODYSSEY
- June is a student taking a statistics course. Unfortunately June is not a diligent student she does not read the textbook before or after class does not do homework and regularly misses class. She intends to rely on log to pass the next quiz. The quiz consists of 10 multiple-choice questions. Each question has five possible answers. Only one of the answers is correct, so the probability of choosing the correct answer is 0.20. June plans to guess the answer to each question independently. Let X be the number of correct answers on June’s quiz. A score (I.e, the number of correct answers) is considered failure if it is less than 6. What is the probability that June fails the quiz?arrow_forwardConsider two types of home insurance: theft insurance and carthquake insurance. Each year there is a 1% chance that the home will be robbed and a 1% chance that the home will be damaged by an canhquake. Suppose an insurance company writes 100,000 policies of each type for homeowners. The risk of earthquake is a type of common risk, while the risk of theft is independent across households. At the beginning of the year, the homeowner expects 1% chance of placing a claim for either type of insurance. However, at the end of the year, the homeowner will have either filled a claim (100%) or not (0%). The standard deviation (expressed in percentage terms) of the claim for an individual homeowner in case of earthquake is kype your answer The standard deviation (expressed in percentage terms) of the claim for an individual homeowner in case of theft is type your answer. The standard deviation (expressed in percentage terms) of the percentage of claims for the insurance company in case of…arrow_forwardA medical study is conducted to determine which migraine treatment, A or B, provides faster relief. The study uses 10 volunteers who claim to suffer from migraines. Half of the volunteers are randomly assigned to use treatment A when they experience their first migraine. The other half are assigned to use treatment B. Then, after no treatment for one month, the treatments are reversed. The volunteers each record the amount of time it takes, in minutes, to experience relief from their migraine under each treatment. The data are displayed in the table. Volunteer 1 2 3 4 5 6 7 8 9 10 Treatment A 10 13 13 9 13 12 14 10 8 7 Treatment B 19 18 19 15 20 16 16 16 13 17 Difference (A – B) –9 –5 –6 –6 –7 –4 –2 –6 –5 –10 The conditions for inference are met. What is the correct 99% confidence interval for the mean difference (A – B) in the time it takes to experience relief? Find the t-table here. (–7.881, –4.119) (–8.314, –3.686) (–8.373, –3.627) (–7.431, –4.569)arrow_forward
- A medical study is conducted to determine which migraine treatment, A or B, provides faster relief. The study uses 10 volunteers who claim to suffer from migraines. Half of the volunteers are randomly assigned to use treatment A when they experience their first migraine. The other half are assigned to use treatment B. Then, after no treatment for one month, the treatments are reversed. The volunteers each record the amount of time it takes, in minutes, to experience relief from their migraine under each treatment. The data are displayed in the table. A 3-column table with 10 rows. Column 1 is labeled volunteer with entries 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Column 2 is labeled Treatment A with entries 10, 13, 13, 9, 13, 12, 14, 10, 8, 7. Column 3 is labeled Treatment B with entries 19, 18, 19, 15, 20, 16, 16, 16, 13, 17. A 99% confidence interval for the mean difference (A – B) in the time it takes to experience relief is –8.37 minutes to 0.732 minutes. Based on the confidence interval,…arrow_forwardA medical study is conducted to determine which migraine treatment, A or B, provides faster relief. The study uses 10 volunteers who claim to suffer from migraines. Half of the volunteers are randomly assigned to use treatment A when they experience their first migraine. The other half are assigned to use treatment B. Then, after no treatment for one month, the treatments are reversed. The volunteers each record the amount of time it takes, in minutes, to experience relief from their migraine under each treatment. The data are displayed in the table. The conditions for inference are met. The 99% confidence interval for the mean difference (A – B) in the time it takes to experience relief is –8.37 minutes to 0.732 minutes. What is the correct interpretation of this interval? The researchers can be 99% confident that the interval from –8.37 minutes to 0.732 minutes captures the true mean time it takes to experience relief. The researchers can be 99% confident that the interval from…arrow_forwardA health researcher studying child birth is interested in the possible effect that smoking by the mother during pregnancy has on the baby's birth weight. To investigate, the researcher conducts an observational study by reviewing 400 records of women in their twenties who have recently given birth for the first time. For each record, he notes whether or not the woman smoked during pregnancy and the baby's birth weight, in addition to the woman's education level, and age. From the data, the researcher creates two groups: women in their twenties who smoked during pregnancy and women in their twenties who did not smoke during pregnancy. Then he compares the average birth weight between the two groups. (a)Why might the researcher have chosen to perform an observational study (by gathering information from past records) and not a randomized experiment (by assigning pregnant women to either the smoking or nonsmoking group at random)? Choose the best answer from the choices below. In a…arrow_forward
- Consider a production system composed of two machines, where only one machine needs to be operational at any given time. The breakdown probability of any operational machine on any given day is 0.2. In case of a machine failure, the production is stopped for the day, and is resumed the next day with the other machine (if available). The repair job of the failed machine also starts the next day. It takes two days to repair a machine, and both machines can be repaired simultaneously.1) Define the state space and draw the state transition diagram.2) Starting with two available machines at the beginning of the first day, what is the probability that both machines are unavailable at the end of the 3rd day?3) In the long run, what is the ratio of the days that both machines are unavailable?arrow_forwardProvide one example of a real-world phenomenon that is well approximated as a Bernoulli trial. Recall that a Bernoulli trial has three requirements: There are only two outcomes, usually called success and failure. The probability of success is constant across trials. The trials are independent. To receive full credit, you must address how your example fulfills these three requirements.arrow_forwardA system contains two components, A and B. The system will function only if both components function. The probability that A functions is 0.98, the probability that B functions is 0.95, and the probability that either A or B functions is 0.99. What is the probability that the system functions?arrow_forward
- A system consists of two components. The probability that the second component functions in a satisfactorymanner during its design life is 0.9, the probability that at least one of the two components does so is 0.96,and the probability that both components do so is 0.75. Given that the first component functions ina satisfactory manner throughout its design life, what is the probability that the second one does also?arrow_forwardA seamstress works exclusively on one stage of the process of a special garment design. This phase requires exactly half an hour to finish the garment. Every 30 minutes an assistant arrives at the seamstress's table to collect those finished garments and deliver those that require the process (unprocessed garments).The number of raw garments brought by the assistant to the seamstress is uncertain; 30% of the occasions arrive without garments; 50% of the time he wears one garment and 20% of the time he wears 2 garments. The assistant is instructed that there are never more than three unprocessed garments left on the seamstress's table (those that cannot be left are taken to another seamstress). Determine the transition graph and matrix that models the number of raw garments on the seamstress's table just before the assistant arrives.arrow_forwardThe probability that a single radar set will detect an enemy plane is 0.85. If we have five radar sets, which independently of each other, find the probability that exactly four sets will detect the plane. at least one set will detect the plane.arrow_forward
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education