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February 27, 2015

February 27, 2015

Posted by **Steven** on Monday, December 16, 2013 at 12:53pm.

According to census statistics, Hispanics comprise 27.5% of the population of New York City. Suppose a random sample of 400 people is selected from New York City. What is the probability that there are fewer than 22% of Hispanics in the sample? Hint: Use Normal approximation to the Binomial distribution.

- Statistics -
**MathGuru**, Monday, December 16, 2013 at 6:46pmUse z-scores.

First problem:

z = (x - mean)/(sd/√n)

Find two z-scores:

z = (2.4 - 2.5)/(0.2/√50) = ?

z = (2.8 - 2.5)/(0.2/√50) = ?

Finish the calculations.

Next, check a z-table to find the probability between the two scores.

Find mean and standard deviation.

mean = np = 400 * .275 = ?

standard deviation = √npq = √(400 * .275 * .725) = ?

Note: q = 1 - p

Finish the calculations.

Next, use z-scores:

z = (x - mean)/sd

z = (.22 - mean)/sd

Substitute the mean and standard deviation into the z-score formula and calculate, then use a z-table to find the probability.

I hope this will help get you started.

- Statistics -
**MathGuru**, Monday, December 16, 2013 at 6:48pmNote: For the second problem, we use the normal approximation to the binomial distribution when finding the mean and standard deviation.

- Statistics -
**Steven**, Tuesday, December 17, 2013 at 7:09pmHow would you check the Z table for the first problem?

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