SUPPOSE X HAS A NORMAL DISTRIBUTION WITH µ= 20 AND σ=4. FIND P( 15 ≤ X ≤ 21
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SUPPOSE X HAS A
FIND P( 15 ≤ X ≤ 21
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- 5. Let X have a nonstandard normal distribution with u=269 and o=23. Find P(X ≤ 278)31. If X is a normal variate with mean 2 and S.D 3, find the X_1. Also find fr 2 distribution of y -1a 3Let 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.
- Assume that Z has a standard normal distribution. Use Appendix Table III to determine the value for z that solves each of the following: a.) P (Z< z)=0.9 b.) P (Z < z ) = 0.5 c.) P (Z < z)=0.1SUPPOSE X HAS A NORMAL DISTRIBUTION WITH µ= 20 AND 0-4. FIND P(15 ≤X ≤21) 0.4931 0.5913 O 0.1934 0.5069Assume the random variable X is normally distributed with a mean of μ=50μ=50and a standard deviation of σ=7.σ=7.Compute and find the probability P(X>35).
- 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.Q1:B B. Let X and Y have a bivariate normal distribution with parameters u, = 3, ly = 1,0 = 16, o, = 25, %3! and p = Suppose that P(c,Assume X has a standard normal distribution (µ = 0, o = 1). Find P(X ≤ 1.2) and P(X ≥ −0.2). (Give your answer to four decimal places.) P(X ≤ 1.2) ≈ P(X ≥ −0.2) ≈When taking random samples of n observations from a population that is not normally distributed, the sampling distribution, x, will be approximately normally distributed never. The population itself must be normally distributed for x to be normally distributed. when the population distribution has low kurtosis. always. when the population standard deviation, o, is greater than n. when n is sufficiently large.Suppose a sample of size n is drawn from a population where the population standard deviation is known. In order to use the Central Limit Theorem, we would have to know that A n > 30 B The population is normally distributed. C n > 30 OR the population is normally distributed D n > 30 AND the population is normally distributedZ is a normally distributed variable with mean μ = 0 and standard deviation σ = 1. Find P(-1 < z < 1.37)SEE MORE QUESTIONS
