A random sample of n = 9 scores is obtained from a normal population with µ = 40 and σ = 6.What is the probability that the sample mean will be greater than M = 43?
A)0.3085
B)0.6915
C)0.9332
D)0.0668

Question

A random sample of n = 9 scores is obtained from a normal population with µ = 40 and σ = 6.What is the probability that the sample mean will be greater than M = 43?​
A)0.3085​
B)​0.6915
C)​0.9332
D)​0.0668

Quizplus · Accepted Answer

Use the formula for the standard error of the mean: 
SE = σ/√n = 6/√9 = 2 
Then, convert the sample mean to a z-score: 
z = (43 - 40)/2 = 1.5 
Finally, use a z-table or calculator to find the probability of a z-score greater than 1.5, which is 0.0668.

A Random Sample of N = 9 Scores Is Obtained