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 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.

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