Question

A population forms a normal distribution with a mean of µ= 40 σ=

12. What is the probability of randomly selecting a sample of n=36
scores with a mean between M=34 and M = 45?

Answer 1

The probability of randomly selecting a sample of size n=36 with a mean between 34 and 45 is approximately 93.19%.

Step-by-step explanation:

To find the probability of randomly selecting a sample of size n=36 with a mean between 34 and 45, we need to calculate the z-scores for both mean values and then use the standard normal distribution table. The z-score for a mean of 34 is (34 - 40) / (12 / sqrt(36)) = -3, and the z-score for a mean of 45 is (45 - 40) / (12 / sqrt(36)) = 1.5. Using the standard normal distribution table, we find the probabilities corresponding to these z-scores to be approximately 0.0013 and 0.9332, respectively. Therefore, the probability of randomly selecting a sample with a mean between 34 and 45 is 0.9332 - 0.0013 = 0.9319, or 93.19%.