Question

In: Statistics and Probability

After years of rapid growth, illegal immigration into the United States has declined because of the...

After years of rapid growth, illegal immigration into the United States has declined because of the recent recession and better economic conditions in the countries south of the border. But California still accounts roughly 20% of the nation undocumented immigrants. If you take a random sample of 50 undocumented immigrants, what is the probability that more than a quarter (25%) of them live in California? (HINT: Large sample proportion – use Normal approximation.) Define p = proportion of all undocumented immigrants who live in California.

A. Is normal approximation appropriate? Why?

B. Mean of the sample proportion is?

C. Standard deviation of the sample proportion is?

D. For , z=?

E. If you take a random sample of 50 undocumented immigrants, what is the probability that more than a quarter (25%) of them live in California?(Hint: check z table)

Solutions

Expert Solution

We can model the given situation using Binomial distribution as follows.

Suppose, random variable X denotes number of illegal immigration in California.

State of immigration of an immigrant is independent of other immigrants.

We define immigrating in California as success.

So, probability of success is 0.20.

A.

We observe that

Hence, Normal approximation is appropriate.

B.

Suppose, random variable Y denotes proportion of undocumented immigrants immigrated in California.

Mean of sample proportion is given by

Hence, mean of the sample proportion is 0.20.

C.

Standard deviation is given by

Hence, standard deviation of the sample proportion is 0.05656854.

D.

From (B) and (C) we obtain

Thus we get,

E.

Required probability is given by

Hence, if we take a random sample of 50 undocumented immigrants, 0.1883796 is the probability that more than a quarter (25%) of them live in California.

orchestra answered 2 years ago
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