If Χ is a random variable that follows a normal distribution, state the following: i. Two...

Question

Question

If Χ is a random variable that follows a normal distribution, state the following:

i. Two properties of the normal distribution

ii. A property that allows us to work out probabilities using half of the distributi

If Z N ∼ (0,1) , find the following probabilities

(i) Ρ Ζ < − ( 1.78)
(ii) Ρ < Ζ < − (0.829 1.843)

(iii) Ρ Ζ < ( 2.326)

math Statistics-And-Probability

Answer 1

Answer #1

Solution :

i)

a) Normal distribution is symmetric distribution .

b) The mean , median and mode are equal .

ii)

P(Z < -1.78) = 0.0375

P(-0.829 < z < 1.843) = P(z < 1.843) - P(z < -0.829) = 0.7638

P(Z < 2.326 = 0.99

Answer 2

Similar Homework Help Questions

2. Random variable Z has the standard normal distribution. Find the following probabilities a): P[Z >...

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...
Which of the following is/are required for the probability distribution of a discrete random variable X...

Which of the following is/are required for the probability distribution of a discrete random variable X with probabilities P(X= x), to be valid? I. PX x) is between 0 and 1 for all values of x. 2aPXx) ii. all x i, all x2 0 Il and Ill only Il only I and Il only I, II, and III only
distribution and finding probabilities using Z-distribution Find the following probabilities (i) P (Z < 1.54) =...

distribution and finding probabilities using Z-distribution Find the following probabilities (i) P (Z < 1.54) = ? (ii) P (Z > 2.15) = ? (iii) P (Z < -1.37) = ?

Problem 1. Let x be a random variable which approximately follows a normal distribution with mean...

Problem 1. Let x be a random variable which approximately follows a normal distribution with mean i = 1000 and o = 200. Use the z-table (attached to this test), calculator, or computer software to find the following: Part A. Find P(> 1500). Part B. Find P(x < 900). Part C. Find P(900<x<1500).
The random variable Z follows a normal distribution with a mean of 0 and a standard...

The random variable Z follows a normal distribution with a mean of 0 and a standard deviation of 1. 1. What is P(Z ≤ -1.54)? Include 4 decimal places in your answer. 2. What is P(Z ≥ 0.45)? Include 4 decimal places in your answer. 3. What is P(-1.25 ≤ Z ≤ 0.65)? Include 4 decimal places in your answer. 4. What is the 45th percentile of Z? That is, what is the value of Z where the cumulative probability...
11. Let z denote a random variable having a standard normal distribution. Determine each of the...

11. Let z denote a random variable having a standard normal distribution. Determine each of the following probabilities. a) P(z < 0.78) b) P(z < −1.25) c) P(z > −1.51) d) P(−0.30 < z < 1.84)

Let z denote a random variable having a normal distribution with μ = 0 and σ...

Let z denote a random variable having a normal distribution with μ = 0 and σ = 1. Determine each of the following probabilities. (Round your answers to four decimal places.) (a) P(z < 0.20) = (b) P(z < −0.20) = (c) P(0.30 < z < 0.86) =
1. (5 points) Suppose Z is a random variable that follows the standard normal distribution. a)...

1. (5 points) Suppose Z is a random variable that follows the standard normal distribution. a) Find P(Z > 0.45). b) Find P(0.7 SZ 1.6). c) Find 20.09. d) Find the Z-score for having area 0.18 to its left under the standard normal curve. e) Find the value of z such that P(-2SZS2) -0.5.
Do the following in the program R Suppose a random variable X follows the Rayleigh distribution...

Do the following in the program R Suppose a random variable X follows the Rayleigh distribution with probability density function given by f(x) = x/sigma^2 e^, 0 lessthanorequalto x < infinity, 0 < sigma < infinity. The cumulative distribution function is F(x) = 1 - e^, 0 lessthanorequalto x < infinity. The mean and variance of a Rayleigh random variable are. respectively. E(X) = sigma squareroot pi/2 and var(X) = (4 - pi/2) sigma^2. Plot the Rayleigh probability density function...

R studio #Exercise : Calculate the following probabilities : #1. Probability that a normal random variable...

R studio #Exercise : Calculate the following probabilities : #1. Probability that a normal random variable with mean 22 and variance 25 #(i)lies between 16.2 and 27.5 #(ii) is greater than 29 #(iii) is less than 17 #(iv)is less than 15 or greater than 25 #2.Probability that in 60 tosses of a fair coin the head comes up #(i) 20,25 or 30 times #(ii) less than 20 times #(iii) between 20 and 30 times #3.A random variable X has Poisson...