What is the least value of k in Chebyshev’s Inequality for which the probability that X assumes a value greater than μ + kσ or less than μ − kσ is less than 0.05
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What is the least value of k in Chebyshev’s Inequality for which the
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- 4. Sixteen-ounce boxes of shredded wheat cereal packed automatically by machine are sometimes over- weight and sometimes underweight. The actual weight in ounces over or under 16 is a random variable X whose probability density is f(x) = c(4- x²) for -2 < x < 2, and 0 elsewhere. Negative values pertain to ounces under 16. Determine the constant c, and then find the probability that a box of cereal will be (a) more than one ounce underweight.How do I solve the following problems?The following table gives the total endothermic reactions involving sodium bicarbonate Final Temperature Conditions Number of Reactions 266 K 271 K 60 274 K 92 Assume that reactions are independent. What is the probability that the 2nd reaction to result in a final temperature less than 272K occurs within three or fewer reactions? Report answer 3 decimal places.
- 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).2. Let X be a random variable with the following probability distribution: -3 6 F(x) | 1/6 1/2 1/3 Find o?gox for the function g(X) = 3x² + 4.If the probability P (a < x < b ) = 0.0395 for the function Y = 3 X 2 and a = 0.15, find the value of b. 0.54 0.35
- The annual rainfall (in inches) in a certain region is normally distributed with µ = 40 and σ = 4. What is the probability that starting with this year, it will take more than 10 years before a year occurs having a rainfall of more than 50 inches? Suppose the rainfall in each year is independent of the rainfall in other years and the distribution of rainfall in each year is the same as in the present year.. The probability that a newborn life (age 0) survives x years is given by: 110 - x xPo 0(50) Let X be a random variable with p.d.f. k 1X P(x) =C p*q"-x %3D When processing credit-card applications there is a 40% chance that an application will have incomplete or insufficient information and require research. You have 5 applications in your to-do pile and would like to leave early today. (a) Fill in the values: n = q = (b) What is the probability of exactly three applications needing research? (enter a number between 0 and 1, 4 decimal places) Answer= (c) What is the expected number of applications that will need research? Answer= (d) What is the probability of having AT LEAST the expected number of applications needing research? (enter a number between 0 and 1, 4 decimal places) Answer= Please answer all parts of the question.Q.No.6.a. A discrete variable ‘X’ has the following probability distributionX -4 -1 1 4 6P(X=x) 0.1 0.4 k 2k 0.2i. Find the value of k.ii. P (x=3)iii. P(x≥1)iv. P(-1≤X<5)b. A bag contains 5 blue and 4 red balls, choose 5 balls randomly, if ‘X’ is the number ofblue balls selected.4. Find the mean of the discrete random variable X with the following probability distribution. Use this formula. μ -ΣΙΧ . P (X)] P(x) х. Р(х) x2 x² . P(x) X 14 1 /½ 5. Referring to the table above, solve for the variance and standard deviation. Use this formula. o² = E[x2 . P(X)1 – µ? E[x² - P(X)] – µ² | O =SEE MORE QUESTIONSRecommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSONA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON