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- Chebyshev's Theorem states that for any set of numbers, the fraction that will like within k Standard deviations of the mean is at least 1- 1/k2. Use this theorem to find the fraxtion of all the numbers of a data that must lie within 3 standard deviations from the mean.Given X~N(50,16) and P(X > 25). The z-score value is: А. С. z = 25 – 50 25 – 50 z = 4 16 50 – 25 D. 50 – 25 z = 4 16 A В Answer: Choose the correct answer. Given X~N(25,25) and P(X > 10). The probability or area under the curve is: A. 0.2257 В. 0.4987 C. 0.9987 D. 0.7257 A D Answer: B. B. B.Q2 It is known that the average mark in a first-year math course exam is normally distributed with a mean of 63 and a standard deviation of 10. Using this information, find 1. The probability that the average exam mark will exceed 75. 2. The probability that the average exam mark will be less than 50. 3. The probability that the average exam mark will lie between 75 and 90. Q3 It is known that the time to failure, in years, of an electronic component is exponentially distributed with λ = 0.2. 1. What is the average time to failure, in years, of this component? 2. Calculate the probability that the time to failure of this component is between 4 and 6 years. 3. What is the expected time to failure of this component if we know it has already lasted 5 years?
- Assume that adults have IQ scores that are normally distributed with a mean of mμ=100 and a standard deviation σ= 15. Find the probability that a randomly selected adult has an IQ less than 127. The probability that a randomly selected adult has an IQ less tha 127 is5. Let Y be a normally distributed random variable with mean = 0 and variance a=1. Use the method of transformation to find the probability distribution of U=Y². What is the name of this distribution?The life of light bulbs is distributed normally. The variance of the lifetime is 900 and the mean lifetime of a bulb is 550 hours. Find the probability of a bulb lasting for at least 583 hours. Round your answer to four decimal places
- 8. Let X be a uniform random variable and P(X7)=0.15. Calculate the mean value and the variance. Find the probability P(X>6).Ryan is throwing a football through a tire in his backyard. He has the probability of .30 of throwing the ball through the tire on each attempt, and each attempt is independent of the one before. Draw the graph of the PDF for the first five attempts. What does the graph tell you about the mean and standard deviation?Suppose the mean monthly return on a T-Bill is 0.5% with a standard deviation of 0.58%. Sup-pose we have another investment Y with a 1.5% mean monthly return and standard deviationof 6%. Which of the two investments o ers less risk in terms of investment.
- Suppose that f (x) = 0.125x for 0 < x < 4 Determine the mean and the variance of X.Suppose that contamination particle size (in microm- eters) can be modeled as f(x)=2x³ for 1 < x. Determine the mean of X. What can you conclude about the variance of X?A random variable follows a normal distribution with mean 12k and variance σ2. The probability that a RV is less than p is 0.9582. knowing that the RV exceeds 10k, the probability that the RV is less than p is 0.95. Calculate σ.