Question

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

Answer 1

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.

Answer 2

I don't understand how to get the answer using the formula.

Answer 3

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

Answer 4

Can you please help me solve for N