After years of rapid growth, illegal immigration into the United States has decl
ID: 3126291 • Letter: A
Question
After years of rapid growth, illegal immigration into the United States has declined, perhaps owing to the recession and increased border enforcement by the United States (Los Angeles Times, September 1, 2010). While its share has declined, California still accounts for 30% of the nation’s estimated 12.1 million undocumented immigrants. Use Table 1. a. In a sample of 50 illegal immigrants, what is the probability that more than 21% live in California? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.) Probability b. In a sample of 250 illegal immigrants, what is the probability that more than 21% live in California? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.) Probability c. Comment on the reason for the difference between the computed probabilities in parts a and b. As the sample number increases, the probability of more than 21% also increases, due to the increased z value and decreased standard deviation As the sample number increases, the probability of more than 21% also increases, due to the increased z value and increased standard deviation
Explanation / Answer
A)
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 0.21
u = mean = p = 0.3
s = standard deviation = sqrt(p(1-p)/n) = 0.064807407
Thus,
z = (x - u) / s = -1.39
Thus, using a table/technology, the right tailed area of this is
P(z > -1.39 ) = 0.9177 [ANSWER]
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b)
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 0.21
u = mean = p = 0.3
s = standard deviation = sqrt(p(1-p)/n) = 0.028982753
Thus,
z = (x - u) / s = -3.11
Thus, using a table/technology, the right tailed area of this is
P(z > -3.11 ) = 0.9991 [ANSWER]
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c)
OPTION A: As the sample number increases, the probability of more than 21% also increases, due to the increased z value and decreased standard deviation.