Question

Given a normal distribution with μ=137 and σ=30, a sample of n=36 is selected. There is a 64% chance that sample mean will be above what value?

a. 147.8
b. 138.8
c. none
d.164.6
e.141.6

Answer 1

To find the sample mean above a certain value, we can use a z-score and the standard normal distribution. The answer is a. 147.8.

Step-by-step explanation:

To find the sample mean above a certain value, we can use a z-score and the standard normal distribution. First, we need to find the z-score for the given probability. Since the probability is 64% or 0.64, the z-score can be found using the inverse normal function: invNorm(0.64, 0, 1) = 0.363. Next, we convert the z-score to the corresponding value on the original distribution using the formula: x = μ + (z * σ). Plugging in the given values, we get x = 137 + (0.363 * 30) = 147.8. Therefore, the answer is a. 147.8.