Chapter 14, Problem 14QP

In designing a new space vehicle, NASA needs to decide whether to provide 0, 1 or 2 backup systems for a critical component of the vehicle. The first backup system, if included, comes into use only if the original system fails.  The second backup system, if included, comes into use only if the original system and the first backup system both fail.  NASA engineers claim that each system, independent of the others, has a 1.5% chance of failing if called into use.  Each backup system costs $70,000 to produce and install within the vehicle.  Once the vehicle is in flight, the mission will be scrubbed (ended early) only if the original system and all backups fail.  The cost of a scrubbed mission, in addition to production costs, is assessed to be $5,000,000.  How many backup systems are needed to minimize NASA’s expected total cost?

WHAT THEY DON'T KNOW WON'T HURT THEM during my last two years in college, I worked for Dan animal hospital in my hometown. In my time there, many animals passed away in their sleep or for unknown reasons. It was not uncommon. In these situations, our facility would offer the owners the service of an autopsy. An autopsy is a procedure in which the doctor would surgically open up the animal to check for any signs of what might have caused the animal's death. Mrs. Johnson, a client of ours, brought in her dog that had unfortunately passed away while she was at work. Her dog was only five years old, and the owners were not aware of any health problems. No one, including the doctor, could figure out what had caused the death of Mrs. Johns on's dog. Mrs. Johnson was asked if she would give her con- sent for the doctor to perform an autopsy on her dog so they might be able to answer the many questions surrounding his death. Mrs. Johnson did not want this procedure to be done; she just wanted…

Suppose that you have two four-sided dice that are each equally weighted (i.e. equal chance of any of the four sides landing face up). One of them has values [12.5968, 2, -2 and -12.5968] , the other [12.5968, 4, -2 and -12.5968] Which of them has a σ of 9 using the probability model approach.   a) [12.5968, 2, -2 and -12.5968]   B) [12.5968, 4, -2 and -12.5968]

A product is composed of four parts. In order for the product to function properly in a given situation, each of the parts must function. Two of the parts have a .96 probability of functioning, and twohave a probability of .99. What is the overall probability that the product will function properly?

None

Bill Hardgrave, production foreman for the Virginia Fruit Company, estimates that the average sales of oranges is 4,700 and the standard deviation is 500 oranges. Sales follow a normal distribution.a) What is the probability that sales will be greater than 5,500 oranges?b) What is the probability that sales will be greater than 4,500 oranges?c) What is the probability that sales will be less than 4,900 oranges?d) What is the probability that sales will be less than 4,300 oranges?

A certain reagent is created to test for an infectious disease. The test has anaccuracy rate of p = 90%, and the accuracy does not depend on whether or not thepatient is actually infected. a. If four people are tested for the disease, what is the probability that at leastthree of them receive accurate test results? b. In an area where q = 5% of people are infected, a man’s test result ispositive. What is probability that it is a false positive (which means that he is notinfected but the test is positive due to inaccuracy)?   *please solve for a-b, type or neatly  write your answers on paper, NO EXCEL* thank you !

Suppose that you have two four-sided dice that are each equally weighted (i.e. equal chance of any of the four sides landing face up). One of them has values [12.5968, 2, -2 and -12.5968] , the other [12.5968, 4, -2 and -12.5968] . Which of them has a µ of zero using the probability model approach.   1. [12.5968, 4, -2 and -12.5968]   2. [12.5968, 2, -2 and -12.5968]

If two variables are highly correlated, does this imply that changes in one cause changes in the other? If not, give at least one example from the real world that illustrates what else could cause a high correlation.