Wiki Page, Math 13 - Perez Sandbox : ANSWER(S): Module 17- Distribution of Sample Proportions (5 of 6 discussion 2)

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2026-01-17T21:14:48-08:00

Here is an example of a correct response to the prompt from the previous Learn by Doing activity.

Conclusion:

The probability is about 0.08. If it is true that 40% of the population of white males voted for Obama in 2000, then it is somewhat unusual to see a random sample of 200 white males with less than 35% supporting Obama.

Here is the detailed work that lead to the correct response above.

Check normality conditions:

and

(The expected number of successes is greater than 10.)

(The expected number of failures is greater than 10.)

Therefore, the conditions are met and we can use a normal model. A normal model allows us to use a Z-score and the Normal Distribution Calculator to find the probability.

Find the Z-score:

Find the probability using the standard normal model:

We want the probability that the sample proportion is less than 35%. So we want the probability that the Z-score is less than -1.43. The shaded region to the left of z = -1.43 is about 0.0764. Rounding to two decimal places gives us a probability of about 0.08.