Use technology to solve the following problem: A sample of size 52 will be drawn from a population with mean 11 and standard deviation 11. Find the probability that $\bar { x }$ will be greater than13
A) 0.1001
B) 0.0667
C) 0.0949
D) 0.9051

Question

Quizplus · Accepted Answer

We can use the central limit theorem and the z-score formula to solve this problem.

First, we find the standard error of the mean:
SE = σ/√n = 11/√52 ≈ 1.519

Next, we calculate the z-score:
z = (x - μ) / SE = (13 - 11) / 1.519 ≈ 1.316

Finally, we use a standard normal distribution table or calculator to find the probability:
P(𝑧 > 1.316) ≈ 0.0949

Therefore, the probability that 𝑥¯ will be greater than 13 is approximately 0.0949.

Use Technology to Solve the Following Problem: a Sample of Size