If the random variable X has a normal distribution with μ = 87 and standard deviation = 6, then P([[X ≥ 73.038) i
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Q: = Normal Distribution with μ P(X> 1.28) = -1.28 -1 0 μ 0 and a = 1 1.28
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Q: if X has a normal distribution with mean -1, and variance 16 then P(x < 2) = O 0.50 O 0.7734 O none…
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Q: If X is normal with mean 9 and variance o? where P(X >7.5) = 0.7734 Then standard deviation of X is
A: The mean of the data is 9. The probability of event is more than 7.5 is 0.7734
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Q: Now for X- N(2,9) the p(-3< X – 2<3) is nearly O 0.28 0.68 O 0.88 0,98
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Q: 3. For a normal population with a mean of 20 and a variance IU, None of the other 0.25 0.50 0.35
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Q: ..If X is a Normal variate with mean30 and D 5.Find P [26<X<40].
A: Given that mean =30 standard deviation=5
If the random variable X has a
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- 1. Consider a Normal Distribution of Mean = 50 and Standard Deviation of 10. D. Approximate the value of T such that P(X > T) = 0.9 E. Approximate the value of T such that P(X>T) = 0.1= 5 and a standard deviation of a = 2. Suppose X is normally distributed with a mean of u Further suppose that a random sample of n = 50 has been taken from this population. Which of the following statements is/are true about the distribution of the associated sample mean, X? Select one or more: O a. The variability of the distribution of X will be higher than the variability of the distribution of X O b. □ C. The distribution of X will have a variance of Oh. √50 The distribution of X will have a standard deviation of 50 Od. The distribution of X will have a mean of μ 5 Of. The distribution of X will be unknown g. The variability of the distribution of X will be lower than the variability of the distribution of X 4 The distribution of X will have a variance of 50A random sample is drawn from a population with mean U= 72 and standard deviation o = 6.0. [You may find it useful to reference the z table.) a. Is the sampling distribution of the sample mean with n= 17 andn= 45 normally distributed? O Yes, both the sample means will have a normal distribution. O No, both the sample means will not have a normal distribution. O No, only the sample mean with n=17 will have a normal distribution. O No, only the sample mean with n= 45 will have a normal distribution, b. Calculate the probability that the sample mean falls between 72 and 75 for n= 45. (Round intermediate calculations to at least 4 decimal places, "z" value to 2 decimal places, and final answer to 4 decimal places.) Probability 1 of 8 Next > ere to search (? A R G B
- Take a=1 in the questionLet 0< a< 1. For a normally distributed variable, show that 100(1 - a)% of all possible observations lie within za/2 standard deviations to either side of the mean, that is, between µ - za/2 • σ and µ + za/2 • σ.7. Assume that X and Y have a bivariate normal distribution having means 14.l and 1.3, and standard deviations 2.5 and 0.1, respectively, with correlation coefficient 0.8. Find P(Y >1.4|X =15) and P(X >15|Y = 1.4).
- Suppose X is a random variable defined as final cost of project estimated cost of project which has a PDF as follows: [0 xa a. Determine the value of a. b. What is the probability that the final cost of a project will exceed its estimated cost by 25%? c. Determine the mean value and standard deviation of X.3. Let X1,X2, ..,X, be a random sample form a normal distribution with E(X;) = µ;and Var(X;) = o². Assume s? = E(X;_ X)²/n and s3 = (n/(n – 1))s?. Questions: a. Compare between the estimators si and s?. b. Which one you preferred? What is (are) your reason(s). 4. Let X1,X2, . X, be a random sample form a uniform distribution, f(X)e = 0*(1– e)!-*; 0 < x < 1. Assume T1 = X1 and T, = (-)Ex;. %3D a. Check the unbiasedness property for T1 and T,. b. Find the MSE of T, and T,. Can you preferer one of them? Discuss your reasons. с. 5. Suppose that X, X2,. , X, are an iid sample from the distribution given below, f(X)e = (1/2)(1+ X8); -1< X <1. Show that 3x is a consistent estimator of e.True or False i. X is an unbiased estimator of u. ii. Sis an unbiased estimator of O. ii. S2 is an unbiased estimator of O2. iv. The standard normal distribution has a mean of 0 and standard deviation of 0. For every possible value of x, 0 < p(x) < 1, Ep(x) = 1. V.
- Recommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON