Question: In a support system in the U.S. space program, a single crucial component works only 85% of the time. In order to enhance the reliability

In a support system in the U.S. space program, a single crucial component works only 85% of the time. In order to enhance the reliability of the system, it is decided that 3 components will be installed in parallel such that the system fails only if they all fail. Assume the components act independently and that they are equivalent in the sense that all 3 of them have an 85% success rate. Consider the random variable X as the number of components out of 3 that fail.
(a) Write out a probability function for the random variable X.
(b) What is E(X) (i.e., the mean number of components out of 3 that fail)?
(c) What is Var(X)?
(d) What is the probability that the entire system is successful?
(e) What is the probability that the system fails?
(f) If the desire is to have the system be successful with probability 0.99, are three components sufficient? If not, how many are required?

Step by Step Solution

★★★★★

3.27 Rating (162 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a b EX 045 c EX 2 0585 so V ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (2 attachments)

1621_606abedd8d5f7_680138.pdf

180 KBs PDF File

1621_606abedd8d5f7_680138.docx

120 KBs Word File

Students Have Also Explored These Related Essentials of Statistics Questions!

An important system acts in support of a vehicle in our space program. A single crucial component works only 85% of the time. In order to enhance the reliability of the system, it is decided that 3...

The U.S. space program has a history of many successes and some failures. Space flight reliability is of the utmost importance in the launching of space shuttles. The reliability of the complete...

The Human Resources Department at Gutierrez and Associates has developed an interviewing procedure for hiring new employees. Prior to the interview, the department head uses the candidates resume to...

In a support system in the U.S. space program, a single crucial component works only 85% of the time. In order to enhance the reliability of the system, it is decided that 3 components will be...

4.94 In a support system in the U.S. space program, a single crucial component works only 85% of the time. In order to enhance the reliability of the system, it is decided that 3 components will be...

In a support system in the U.S. space program, a single crucial component works only 85% of the time. In order to enhance the reliability of the system, it is decided that 3 components will be...

Help on Financial Statement analysis homework, need a perfect solution to improve grade UNITED STATES SECURITIES AND EXCHANGE COMMISSION Washington, D.C. 20549 Form 10- K (Mark One) 3 ANNUAL REPORT...

Lesson 12 Quiz (Show/Explain all Work) IST 230 Relations on Sets, Databases 1. Let A = {0, 1, 2, 3, 4, 5, 6, 7, 8} and B = {1, 2, 3, 4, 5, 6, 7, 8}. Now let R be a binary relation R from A to B such...

currency) will play a dominant role in the world and will - possibly - replace some previously established businesses (if not the whole markets). But - to achieve such a supremacy - changes are...

Hi I was wondering If someone can check my ratios. I had to do the ratios for two companies for years 2015 and 2014. Can you please check them for me and let me know if there is anything wrong and...

Albert Gaytor and his wife Allison are married and file a joint return for 2019. The Gaytors live at 12340 Cocoshell Road, Coral Gables, FL 33134. Captain Gaytor is a charter fishing boat captain but...

Find the binding energy of an electron in the ground state of hydrogen-like ions in whose spectrum the third line of the Balmer series is equal to 108.5 nm.

Question 3 On January 1 , the euro is worth $ 1 . 1 3 0 5 . By March 1 , it has moved to $ 1 . 1 1 2 5 . a . By how much has the euro appreciated or depreciated against the dollar over this 2 - month...

A recently admitted class of graduate students at a large state university has a mean Graduate Record Exam verbal score of 650 with a standard deviation of 50. (The scores are reasonably normally...

Iranian researchers studied factors affecting patients likelihood of wearing orthodontic appliances, noting that orthodontics is perhaps the area of health care with the highest need for patient...

In an example we sometimes use in our statistics classes, several semesters worth of male and female students were asked how long, in minutes, they spend getting ready for a date. The data reported...

Are Women Really More Talkative Than Men? is the title of an article that appeared in the journal Science. In the article, Mehl, Vazire, Ramirez- Esparza, Slatcher, & Pennebaker (2007) report the...

On the graduate record exam in economics, scores are normally distributed with a mean of 615 and a standard deviation of 107. If a college admissions office decides to require scores above the 70 th...

Lottery games are very popular, but what are the actual probabilities that a ticket purchased is going to win? Calculate the probability of winning some of the more popular games. A game that draws 3...

Consider a Black-Scholes model with r = 6%, sigma = 0.25, S(0) = 50 and delta = 0. Suppose you sold ten (10) 90-day Puts with strike K = 50 (at price C_1(0) determined by the Black-Scholes formula)....