Question

"Given a random variable X ~N(10, 18) and n = 64 finish thefollowing problems.

A) The mean of x-bar = ________
B)The variance of x-bar = __________________
C)The standard deviation of x-bar = _______________
D) x > N( (Hint what is the mean of xbar and what is the variance of xbar)

Answer 1

A) The mean of x-bar = 10. B) The variance of x-bar = 0.28125. C) The standard deviation of x-bar = 0.5303. D) Use a standard normal distribution table to find the probability of x > N.

Step-by-step explanation:

A) The mean of x-bar is the same as the mean of the original random variable X, which is 10.

B) The variance of x-bar is the variance of the original random variable divided by the sample size, which is 18/64 = 0.28125.

C) The standard deviation of x-bar is the square root of the variance of x-bar, which is sqrt(0.28125) = 0.5303.

D) To find the probability that x > N, we can calculate the z-score for the value of x and use a standard normal distribution table.