Posted by angela on Monday, October 15, 2012 at 1:20am.
random sample of n = 16 scores is selected from a normal distribution with a mean of μ = 50 and standard deviation of σ = 10.
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?

statistics  MathGuru, Monday, October 15, 2012 at 7:36pm
Find zscores using sample size:
z = (x  mean)/(sd/√n)
For a):
x = 45, 55
mean = 50
sd = 10
n = 16
Find two zscores, using the values above. Use a ztable to find the probability between the two scores.
For b):
x = 48, 52
mean = 50
sd = 10
n = 16
Find two zscores, using the values above. Use a ztable 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.
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