Statistics

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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.

• Statistics -

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 z-scores:

z = (x - mean)/sd

Therefore:

z = (41.36 - 39.292)/(6.025) = 0.34

Check a z-table for the probability using the z-score calculated above. Remember that the problem is asking "less than" when looking at the table.

I hope this helps.

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