A sample of size 42 will be drawn from a population with mean 34 and standard deviation 8. Find the probability that $\bar { x }$ will be greater than 36 .
A) 0.0526
B) 0.9474
C) 0.0749
D) 0.0351

Question

A sample of size 42 will be drawn from a population with mean 34 and standard deviation 8. Find the probability that $\bar { x }$ will be greater than 36 .
A)  0.0526 
B)  0.9474 
C)  0.0749 
D)  0.0351

Quizplus · Accepted Answer

To find the probability that $\bar{x}$ will be greater than 36, we use the Central Limit Theorem. The standard error (SE) of the sample mean is $\sigma/\sqrt{n} = 8/\sqrt{42}$. We calculate the z-score for $\bar{x} = 36$ as $z = (36 - 34) / (8/\sqrt{42})$. Using the z-score, we find the probability from the standard normal distribution table, which gives us approximately 0.0526.

A Sample of Size 42 Will Be Drawn from a Population