In a certain city, the daily consumption of water (in millions of liters) follows approximately a gamma distribution with a = 4 and ẞ=2. If the daily capacity of that city is 4 million liters of water, what is the probability that on any given day the water supply is inadequate?
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- A person's blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean u = 86 and standard deviation o = 26. Note: After 50 years of age, both the mean and standard deviation tend to increase. For an adult (under 50) after a 12-hour fast, find the following probabilities. (Round your answers to four decimal places.) A USE SALT (a) x is more than 60 0.8315 (b) x is less than 110 (c) x is between 60 and 110 (d) x is greater than 125 (borderline diabetes starts at 125)6. The magnitude (Richter scale) of earthquake along a Taiwanese fault is exponentially distributed, with A= (1/2.5). What is the probability of an earthquake exceeding magnitude 6.4? There is 1 earthquake per year (on average) along the fault with magnitude greater than 5.5. Given this, what is the probability of an earthquake during the year that exceeds magnitude 7.2?The magnitudes of earthquakes recorded in a region of North America can be modeled by an exponential distribution with a mean of 2.4 as measured on the Righter scale. Of the next 10 earthquakes to strike this region, find the probability that at least one will exceed 5.0 on the Richter scale.
- The lifetime, in years, of a certain type of electrical switch has an exponential distribution withan average lifetime of 2 years. Question. For a single system, what is the probability we can keep one switching mechanismoperable for 10 years if we assume we can replace a switch due to failures up to three timesduring the 10-year period?The manager of a supermarket tracked the amount of time needed for customers to be served by the cashier. After checking with his statistics professor, he concluded that the checkout times are exponentially distributed with a mean of 5 minutes. What propotion of customers require more than 10 minutes to check out?An article in a magazine discussed the length of time till failure of a particular product. At the end of the product's lifetime, the time till failure is modeled using an exponential distribution with a mean of 500 thousand hours. In reliability jargon this is known as the "wear-out" distribution for the product. During its normal (useful) life, assume the product's time till failure is uniformly distributed over the range 200 thousand to 1 million hours. Complete parts a through c. a. At the end of the product's lifetime, find the probability that the product fails before 600 thousand hours. (Round to four decimal places as needed.)
- Suppose that the time to failure (in hours) of fans in a personal computer can be modeled by an exponential distribution with A = 0.0003. • What proportion of the fans will last at most 10,000 hours? • What proportion of the fans will last at least 7000 hours? a. 0.0498, 0.8775 Ob. NONE Oc 0.0498, 0.1225 Od.0.0502, 0.1225The lifetime T (in years) for a particular type of electric toothbrush is assumed to have the probability density f given by t 0 ≤ t ≤6 f(t) = {+ 3 18 otherwise.b. The lifetime X of a particular species is assumed to be exponentially distributed with mean 75 time units. Find the probability that a member of this particular species picked at random survives: i. more than 90 time units; less than 70 time units; between 70 and 85 time units. ii. iii. iv. Calculate Var(X).
- Two geysers that are near to each other are labelled as Geyser A and Geyser B. The time between eruptions for a given geyser follows an exponential distribution. The eruption times of the two geysers are independent of one another. The mean amount of time between eruptions of Geyser A is 39 minutes, and the mean amount of time between eruptions of Geyser B is 66 minutes. Given that exactly one of the geysers erupts within the next 49 minutes, determine the probability that it will be Geyser A. O 0.6654 0.7850 O 0.7252 O 0.6953 O 0.75515. A pressure transducer regulates a climate control system in a factory. The transducer fails according to an exponential distribution with rate one failure every five years on average. a. What is the cumulative distribution function of the time until failure? b. What is the probability that a transducer chosen at random functions for eight years without failure? irteen Reliability and Maintainability c. What is the probability that a transducer that has functioned for eight years con- tinues to function for another eight years?Suppose that the number of traffic accident claims received in a month is modeled by Poisson distribution with intensity λ = 4. Assume that each traffic accident claim takes values $150, $300 or $450 equally likely. Calculate the probability that the total traffic accident claim amounts to exactly $1500.
