Posted by **Desire** on Wednesday, November 25, 2009 at 12:02pm.

Assume we draw a simple random sample from a population having a mean of 100 and a standard deviation of 16. What is the probability that a sample mean will be within plus-or-minus two of the population mean for each of the following sample sizes?

n = 50

n=100

n=200

n=400

- Stats -
**PsyDAG**, Thursday, November 26, 2009 at 7:22am
The probability of being within Z = ±2 for a normal distribution always approximates 95%. However, what you might be seeking is the high and low values that cut off that proportion.

Standard error of the mean (SE) = standard deviation/square root of n

Z = (raw score - mean)/SE

±2 = (raw score - 100)/SE

Use the four SEs to find the raw score (±).

I hope this helps.

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**Desire**, Saturday, November 28, 2009 at 2:33am
I don't understand how to get the answer using the formula.

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**Desire**, Monday, November 30, 2009 at 12:25pm
For n = 100:

Lower limit: 100 - 2*16/sqrt(100) = 96.8

Upper limit: 100 + 2*16/sqrt(100) = 103.2

I can't get the answer for the other ones

- Stats -
**Desire**, Tuesday, December 1, 2009 at 1:12pm
Can you please help me solve for N

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