For Questions 1-4, let the random variable X follow a Normal distribution with mean u =...
Sampling Distributions For Questions 6 - 8, let the random variable X follow a Normal distribution with variance σ2 = 625. Q6. A random sample of n = 50 is obtained with a sample mean, X-Bar of 180. What is the probability that population mean μ is greater than 190? a. What is Z-Score for μ greater than 190 ==> b. P[Z > Z-Score] ==> Q7. What is the probability that μ is between 198 and 211? a. What is...
Suppose that Xi are IID normal random variables with mean 2 and variance 1, for i = 1, 2, ..., n. (a) Calculate P(X1 < 2.6), i.e., the probability that the first value collected is less than 2.6. (b) Suppose we collect a sample of size 2, X1 and X2. What is the probability that their sample mean is greater than 3? (c) Again, suppose we collect two samples (n=2), X1 and X2. What is the probability that their sum...
Let the random variable X follow a normal distribution with u = 20 and o2 = 11. Find the probability that X is greater than 23 and less than 28.
A population of values has a normal distribution with μ=30.9μ=30.9 and σ=70.2σ=70.2. You intend to draw a random sample of size n=211 Find the probability that a single randomly selected value is greater than 28.5. P(X > 28.5) =_____ Find the probability that a sample of size n=211n=211 is randomly selected with a mean greater than 28.5. P(M > 28.5) = _____ Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded...
Let X bar be the sample mean of 25 independent normal random variables with mean u and variance 9. Find the value of u so that: p{X bar<1.5} = 0.85
1. The random variable X is Gaussian with mean 3 and variance 4; that is X ~ N(3,4). $x() = veze sve [5] (a) Find P(-1 < X < 5), the probability that X is between -1 and 5 (inclusive). Write your answer in terms of the 0 () function. [5] (b) Find P(X2 – 3 < 6). Write your answer in terms of the 0 () function. [5] (c) We know from class that the random variable Y =...
1. Let X be a normal random variable with mean 16. If P(X < 20) 0.65, find the standard deviation o. 2. The probability that an electronic component will fail in performance is 0.2 Use the normal approximation to Binomial to find the probability that among 100 such components, (a) at least 23 will fail in performance. X 26) (b) between 18 and 26 (inclusive) will fail in performance. That is find P(18 3. If two random variables X and...
Let X be a random variable with a normal distribution having a mean of 30 and a known standard deviation of 16. What is the probability that X is greater than 50? A- 0.1056 B- 0.6057 C- 0.3944 D- 0.8944
6.33 Let x be a continuous random variable that is normally distributed with a mean of 25 and a standard deviation of 6. Find the probability that x assumes a value a. between 28 and 34 b. between 20 and 35 6.34 Let x be a continuous random variable that has a normal distribution with a mean of 30 and a stan- dard deviation of 2. Find the probability that x assumes a value a. between 29 and 35 b....
Let the random variable X follow a normal distribution with a mean of μ and a standard deviation of σ. Let X 1 be the mean of a sample of 36 observations randomly chosen from this population, and X 2 be the mean of a sample of 25 observations randomly chosen from the same population. a) How are X 1 and X 2 distributed? Write down the form of the density function and the corresponding parameters. b) Evaluate the statement:...