1. Let 2 ~ N (0,1). Using a standard normal table, find the following probabilities. You...
Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures whenever appropriate. (Do this on paper. Your instructor may ask you to turn in this work.) (a) P(0 Z 2.74) (b) P(0 Z 1) (c) P(-2.40 Z 0) (d) P(-2.40 Z +2.40) (e) P(Z 1.63) (f) P(-1.74 Z) (g) P(-1.4 Z 2.00) (h) P(1.63 Z 2.50) (i) P(1.4 Z) (j) P( |Z| 2.50) Let Z be a standard normal random variable and calculate the following...
Find the following probabilities based on the standard normal variable Z. (You may find it useful to reference the z table. Leave no cells blank - be certain to enter "0" wherever required. Round your answers to 4 decimal places.) a. P(−1.12 ≤ Z ≤ −0.63) b. P(0.05 ≤ Z ≤ 1.65) c. P(−1.47 ≤ Z ≤ 0.09) d. P(Z > 3.5)
2. Random variable Z has the standard normal distribution. Find the following probabilities a): P[Z > 2] b) : P[0.67 <z c): P[Z > -1.32] d): P(Z > 1.96] e): P[-1 <Z <2] : P[-2.4 < Z < -1.2] g): P[Z-0.5) 3. Random variable 2 has the standard normal distribution. Find the values from the following probabilities. a): P[Z > 2) - 0.431 b): P[:<] -0.121 c): P[Z > 2] = 0.978 d): P[2] > 2] -0.001 e): P[- <Z...
1. Use Appendix Table III to determine the following probabilities for the standard normal variable Z. a) P(-0.7<Z< 0.7) b) P(-1.5<Z<1.5) c) P(-2.0<Z<2.0) d) P(Z>2.0)=
9. Compute the following probabilities using your calculator. Assume Z is a standard normal random variable. Round all answers to three decimal places. A. P(0<Z<2.3)P(0<Z<2.3)= B. P(−1.7<Z<0.15)P(−1.7<Z<0.15)= C. P(Z>−1.2)P(Z>−1.2)= 10. Find the following probabilities for the standard normal random variable zz: Round answers to three decimal places. (a) P(z≤1.31)=P(z≤1.31)= (b) P(z>−0.25)=P(z>−0.25)=
2. Let Z~ N(0,12) (distributed as a standard normal rv). Calculate the following probabilities, show your R code, and shade in the probability for plots that are missing it (do the shading by hand). a. P(0<Z<2.17)? Standard Normal 0.4 0.3 f(x0,1) 0.2 0.1 4TTT -3 -2 -1 0 1 2 3 b. P(-2.5 <Z <0)? Standard Normal 0.4 0.3 f(x:0,1) 0.2 0.1 0.0 LC - -3 -2 -1 0 1 2 C. P(-2.5 <Z< 2.5)? Standard Normal 0.4 0.3 f(x;0,1)...
Use the Standard Normal table to find the following probabilities. (Keep probabilities at 4 decimal places.) P(-1.49< z < 2.04) =
(1 point) Find the following probabilities for the standard normal random variable z. (a) P(-0.81 <<0.42) (b) P(-1.14 <z < 0.5) (c) P(Z < 0.69) a (d) P(Z > -0.6)
2. Approximate the following probabilities for sufficiently large n by applying CLT. Please provide answers using the standard CDF Φ(z) = P(Z 2) where Z ~ N(0,1), instead of real numbers. (a) For X Binomial(n, 1/4), P(X/Vn 0.5). (b) For X1, , , , Xn iid Uniform(0, 1), PK, < 2/(3 ) (c) For Y ~ χ2(n), P(Y < n).
Find the following probabilities based on the standard normal variable Z. (You may find it useful to reference the z table. Leave no cells blank - be certain to enter "0" wherever required. Round your answers to 4 decimal places.) Find the following probabilities based on the standard normal variable Z. (You may find it useful to reference the z table. Leave no cells blank - be certain to enter "O" wherever required. Round your answers to 4 decimal places.)...