random sample of n = 16 scores is selected from a normal distribution with a mean of μ = 50 and standard deviation of σ = 10.

Question

a. what is the probability that the sample mean will have a value between 45 and 55?
b. what is the probability that the sample mean will have a value between 48 and 52?
c. what range of values contains the middle 95% of all possible sample means for n = 16?

Answer 1

Find z-scores using sample size:

z = (x - mean)/(sd/√n)

For a):
x = 45, 55
mean = 50
sd = 10
n = 16

Find two z-scores, using the values above. Use a z-table to find the probability between the two scores.

For b):
x = 48, 52
mean = 50
sd = 10
n = 16

Find two z-scores, using the values above. Use a z-table to find the probability between the two scores.

For c):
-1.96 = (x - 50)/(10/√16)
1.96 = (x - 50)/(10/√16)

Solve both equations for x. Those values will be your range of values containing the middle 95%.

I hope this will help get you started.