posted by Paul .
An April 15, 2002 report in Time Magazine stated that the average age for women to marry in the United States is now 24.5 years of age. If the standard deviation is assumed to be 4.1 years, find the probability that a random sample of 32 U.S. women would show a mean age at marriage of less than or equal to 22.7 years.
Use this formula for z-scores:
z = (x - mean)/(sd/√n)
With the data from your problem:
z = (22.7 - 24.5)/(4.1/√32) = ?
Finish the calculation.
Next, look at a z-table to find your probability. Remember that the problem is asking for "less than or equal to" when looking at the table.
I hope this helps.