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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 -

    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.

  • Stats -

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

  • Stats -

    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 -

    Can you please help me solve for N

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