Question

Suppose we use iid sampling to obtain a sample of size 16 from a normal population with standard deviation, sigma = 10. What is the probability that our sample mean will be within 2 of the population mean?

Answer 1

"The structural of population mean for known sample mean is given by, u = x^barplusminus Z_(1 - alpha/2) times 3/squareroot n also , s = 5/squareroot n Now, n = 16, sigma = 10 s = 10/squareroot 16 = 10/4 Now, Mu = x^barplusminus Z_(1 - alpha_2) times 10/4 times squareroot 16. Mu - x^bar = plusminus Z (1 - alpha_2) 10/4 times 4