Every Thursday, Matt and Dave’s Video Venture has “roll-the-…
Every Thursday, Matt and Dave’s Video Venture has “roll-the-dice” day. A customer may choose to roll two fair dice and rent a second movie for an amount (in cents) equal to the numbers uppermost on the dice, with the larger number first. For example, if the customer rolls a two and a four, a second movie may be rented for $0.42. If a two and a two are rolled, a second movie may be rented for $0.22. Let X represent the amount paid for a second movie on roll-the-dice day. The expected value of X is $0.47 and the standard deviation of X is $0.15. If a customer rolls the dice and rents a second movie every Thursday for 20 consecutive weeks, what is the total amount that the customer would expect to pay for these second movies?
Read DetailsTable 1: Thermal vs. Voltage Failure Results (all 500 compon…
Table 1: Thermal vs. Voltage Failure Results (all 500 components) Voltage Failure No Voltage Failure Total Thermal Failure 50 85 135 No Thermal Failure 65 300 365 Total 115 385 500 Additionally the engineer reports: 70 components experienced a mechanical failure 40 of the components with mechanical failure also had a thermal failure 40 of the components with mechanical failure also had a voltage failure 10 components experienced all three failure types simultaneously Let A = thermal failure, B = voltage failure, C = mechanical failure What is the probability that a randomly selected component experiences exactly two types of failure?
Read DetailsTable 1: Thermal vs. Voltage Failure Results (all 500 compon…
Table 1: Thermal vs. Voltage Failure Results (all 500 components) Voltage Failure No Voltage Failure Total Thermal Failure 50 85 135 No Thermal Failure 65 300 365 Total 115 385 500 Additionally the engineer reports: 70 components experienced a mechanical failure 40 of the components with mechanical failure also had a thermal failure 40 of the components with mechanical failure also had a voltage failure 10 components experienced all three failure types simultaneously Let A = thermal failure, B = voltage failure, C = mechanical failure A screening test for thermal failures has 92% sensitivity(detects components that actually have thermal failures,92% of the time) and an 8% false positive rate. Using the Law of Total Probability, what is the overall probability that a randomly selected component tests positive on the screening test?
Read DetailsA complex electronic device contains three components, A, B,…
A complex electronic device contains three components, A, B, and C. The probabilities of failure for each component in any one year are: 0.1, 0.05, 0.1, respectively. If any one component fails, the device will fail. If the components fail independently of one another, what is the probability that the device will not fail in one year?
Read DetailsThe heights of adult women are approximately normally distri…
The heights of adult women are approximately normally distributed about a mean of 65 inches with a standard deviation of 2 inches. If Rachel is at the 99th percentile in height for adult women, then her height, in inches, is closest to
Read Details