In a certain city, the daily consumption of electric power, in millions of kilowatt-hours, is a random variable \( X \) having a gamma distribution with mean 6 and variance 12.(a) Find the values of \( \alpha \) and \( \beta \).(b) Find the probability that on any given day the daily power consumption will exceed 11 million kilowatt-hours.

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Answered: In a certain city, the daily…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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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 ? = 81 and standard deviation ? = 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) x is more than 60(b) x is less than 110(c) x is between 60 and 110(d) x is greater than 125 (borderline diabetes starts at 125)
A person's blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter of blood. After a 12-hour fast, the random variable x will have a distribution that is approximately normal with μ = 85 and σ = 25. After 50 years of age, both the mean and standard deviation tend to increase. What is the probability that, for an adult under 50 years old, after a 12-hour fast, x is less than 130?
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 ? = 87 and standard deviation ? = 22. 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.) (c) x is between 60 and 110 (d) x is greater than 125 (borderline diabetes starts at 125)
Suppose a random sample of 25 students is selected from a community college where the scores on the final exam (out of 125 points) are normally distributed having mean equal to 112 and standard deviation equal to 4. Find the probability that the sample mean deviates from the population mean µ = 112 by no more than 3.
Prob and stat
When a random variable X follows binomial distribution, the probability of success on one trian is equal to 0.6, and the number of trials is eual to 120, What is the variance of X ? |------
The Weibull distribution is widely used in statistical problems relating to aging of solid insulating materials subjected to aging and stress. Use this distribution as a model for time (in hours) to failure of solid insulating specimens subjected to AC voltage. The values of the parameters depend on the voltage and temperature; suppose a = 2.6 and B = 220. (a) What is the probability that a specimen's lifetime is at most 250? Less than 250? More than 300? (Round your answers to five decimal places.) at most 250 less than 250 more than 300 0.7520 0.7520 0.1065 x X X (b) What is the probability that a specimen's lifetime is between 100 and 250? (Round your answer to four decimal places.) 0.6312 (c) What value (in hr) is such that exactly 50% of all specimens have lifetimes exceeding that value? (Round your answer to three decimal places.) 191 Xhr
Two airplanes are flying in the same direction in adjacent parallel corridors. At time t = 0, the first airplane is 10 km ahead of the second one. Suppose the speed of the first plane (km/hr) is normally distributed with mean 545 and standard deviation 9 and the second plane's speed is also normally distributed with mean and standard deviation 525 and 9, respectively. (a) What is the probability that after 2 hr of flying, the second plane has not caught up to the first plane? (Round your answer to four decimal places.)(b) Determine the probability that the planes are separated by at most 10 km after 2 hr. (Round your answer to four decimal places.)
A person's blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter of blood. After a 12-hour fast, the random variable x will have a distribution that is approximately normal with μ = 85 and σ = 25. After 50 years of age, both the mean and standard deviation tend to increase. What is the probability that, for an adult under 50 years old, after a 12-hour fast, x is more than 60?
A proton emitter produces proton beams with changing kinetic energy that is uniformly distributed between three and eight joules. Suppose that it is possible to adjust the upper limit of the kinetic energy (currently set to eight joules). • What is the mean kinetic energy? What is the variance of the kinetic energy? What is the probability that a proton beam has a kinetic energy of exactly 3.5 joules? a. E(X) = 5.5, V(X) = 2.0833, probability is zero (0) because X has a continuous distribution O b. E(X) = 5, V(X) = 1.33, probability is zero (0) because X has a uniform distribution O c. NONE O d. E(X) = 5.5, V(X) = 2.0833, probability is zero (0) because X has a uniform distribution

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