Statistics
posted by Steven on .
Suppose that 7.6% of all people are allergic to the H1N1 vaccine. A sample of 517 people are selected
a. Calculate the probability that less than 8% of the sample will be allergic to vaccine.

Mean = np = 517 * .076 = 39.292
Standard deviation = √npq = √(517 * .076 * .924) = √(36.3058) = 6.025
Note: q = 1  p
x = .08 * 517 = 41.36
Use zscores:
z = (x  mean)/sd
Therefore:
z = (41.36  39.292)/(6.025) = 0.34
Check a ztable for the probability using the zscore calculated above. Remember that the problem is asking "less than" when looking at the table.
I hope this helps.