Suppose that Z - N(0,1) so that μ= E(Z)=0 and o²=V(Z)=1. Use the standard Normal Distribution Table to find: a) Pr(Z≤1.645) = (1.645)=. b) a 0.05 such that Pr(Z≤ 0.05) = 0.05, 2005 = c) a = 0.975 such that Pr(ZZ0.975) = 0.95, 20.975 =
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- Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1.If P(−b<z<b)=0.9866P(-b<z<b)=0.9866, find b.b=b=Let X and Y have a bivariate normal distribution with μ = 70, X Find (a) E(Y|X= 76) (b) Var(Y | X= 76) (c) P (Y≤ 861X=76) 0²: X = 100, = 80, My o² = 169, and p=5/13.Let a = 0.05. (a) Suppose that we sample from a bivariate normal distribution with p = 0.5. Assuming that we observe r = 0.5, how large a sample will be needed to reject Ho: p= 0 in favor of Ho: p=0? (b) Suppose that we sample from a bivariate normal distribution with p = 0.1. Assuming that we observe r = 0.1, how large a sample will be needed to reject Ho: p= 0 in favor of Ho: p0?
- Suppose that X-bin(65,0.2). Using the normal approximation to the binomlal distribution, P(12.< X < 14.) is closest to: O a. 0.30 O b.0.26 Oc.0.36 O d. 0.24 O e. 0.18 ity Jump to... 21Let X be a normally distributed random variable with mean u = 27 and standard deviation o = 2. Calculate P(X < 21). Calculate P(25A normal distribution has μ = 30 and σ = 5. (a) Find the z score corresponding to x = 25. (Enter an exact number.) (b) Find the z score corresponding to x = 44. (Enter a number.) (c) Find the raw score corresponding to z = −3. (Enter an exact number.) (d) Find the raw score corresponding to z = 1.5. (Enter a number.)If a random variable X follows normal distribution with mean 10 and standard deviation 50, write down its p.d.f. Also calculate P(X 10). -x? 2 e |Given: 4(1.96) = 0.975, þ(2.36) = 0.99, where (Z) = -dz] ov2nA population of values has a normal distribution with μ=139.8μ=139.8 and σ=54.4σ=54.4. You intend to draw a random sample of size n=87n=87.a.) Find the probability that a single randomly selected value is greater than 121.1.P(X > 121.1) = b.) Find the probability that a sample of size n=87n=87 is randomly selected with a mean greater than 121.1.P(M > 121.1) = (Here M is the mean of the sample)Enter your answers as numbers accurate to 4 decimal places.3) Suppose test scores are measured by the Gaussian Normal Distribution N(X,75,10) calculate the following. a) Pr(80 < X < 90) b) Pr(50 < X < 70) c) The 95 th percentileThe random variable x has a normal distribution with mean 50 and variance 9. Find the value of x, call it x0, such that: a) P(x ≤ xo) = 0.8413 b) P(x > xo) = 0.025 c) P(x > xo) = 0.95 d) P(41 ≤ x ≤ xo) = 0.8630Let zz denote a variable that has a standard normal distribution. Determine the value z∗z∗ to satisfy the following conditions: (a) P(z>z∗)=.7642P(z>z∗)=.7642 (b) P(z<z∗)=.937P(z<z∗)=.937 (c) P(z>z∗orz<−z∗)=0.03Q2: Let X and Y have a bivariate normal distribution with parameters 4, = 2 = 1, of = 16, af = 25 and p = 3. The value of P(-3SEE MORE QUESTIONSRecommended 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