For a normal population with a mean of µ = 80 and a standard deviation of σ = 10,what is the probability of obtaining a sample mean greater than M = 75 for a sample of n = 25 scores?
A)0.0062
B)0.9938
C)0.3085
D)0.6915

Question

Quizplus · Accepted Answer

To find the probability of obtaining a sample mean greater than 75, we use the formula for the standard error of the mean (σM = σ / √n) which in this case is 10 / √25 = 2. Then, we calculate the z-score for M = 75, which is (75 - 80) / 2 = -2.5. Looking up this z-score in a standard normal distribution table or using a calculator, we find the probability of a z-score less than -2.5. Since we want greater than 75, we look for the complement of this, which gives us 0.9938.

For a Normal Population with a Mean of µ =