Problem 1 (16 points). Suppose that Y is normally distributed random variable with u-10 and σ-2...
Random variable X is normally distributed with mean 10 and standard deviation 2.Compute the following probabilities.a. Pr(X<10) b. Pr(X<11.04)I don't know where to start.
of the random variable x. Suppose x is a normally distributed random variable with u = 34 and 0 = 4. Find a value a. P(x 2 Xo)=5 b. P(X<Xo) = .025 c. P(x>x) = 10 d. P(x > Xo) = .95 Click here to view a table of areas under the standardized normal curve. a. Xo = (Round to the nearest hundredth as needed.)
Suppose a random variable x is normally distributed with μ = 17.5 and σ = 5.8 . According to the Central Limit Theorem, for samples of size 8: The mean of the sampling distribution for x¯ ( x bar ) is: 1
The random variable X is normally distributed with μ = 72.3 and σ = 8.75. What value of X will be exceeded 12% of the time? (This is the 88th percentile of X.) Round your answer to one place of decimal
2. Find each of the following probabilities. Suppose x is a normally distributed random variable with-11 and ơ a. P(x2 14.5) b. P(xs 10) c.P/12.26sxs 16.02) d. P(5.5sxs14.48) Click here to view a table of areas under the standardized normal curve. a. P/xz 14.5)-(Round to three decimal places as needed.)
Problem 2. (26 points) Two random variables X and Y are jointly normally distributed, with E(X)x, EY) y and co-variance Cov(X,Y) = ơXY. To estimate the population co-variance ơXY, a very simple random sample is drawn from the population. This random sample consists of n pairs of random variables {OG, Yİ), (XyW), , (x,,y,)). Based on the sample, we construct sample co-variance SXY as: Ti-1 2-1 1. (4 points) Show Σ(Xi-X) (Yi-Y) = Σ Xix-n-X-Y. 2. (4 points) Find E(Xi...
Exercise 2. Let consider a normally distributed random variable Z with mean 0 and variance 1. Compute (a) P(Z < 1.34). (b) P(Z > -0.01). (c) the number k such that P(Z <k) = 0.975.
For a normal random variable, with μ = 20, and σ = 2, find the following probabilities. (a) Pr(X ≤ 21.1) (b) Pr(X > 15.90)
1 point) Suppose X is a normally distributed random variable with H9 and ơ 1.3. Find each of the following probabilities: (a) P(12 < X < 15) (b) P(6.1 K X K 16.7)- (c) P(11.1 K X K 16.7)- (d) P(X 2 11.5)- (e) P(X s 16.7)-
(1 point) Suppose z is a normally distributed random variable with u = 10.6 and o = 1.6. Find each of the following probabilities: (a) P(8.6 << < 15.1) (b) P(5.1 5*< 15.8) (c) P(7.1 Su 15.9) (d) P(x > 5.3) = (e) P(x< 13.4) =