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Siqi C.

Graduated Student

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GRE

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Question:

2a + b = 17 b - 3 = 2 what is a and what is b ?

Siqi C.

Answer:

from the second equation b-3=2 then b=5 then 2a+b=17, we take b=5 into the equation 2a+5=17 then 2a=12 , that is a=6

Statistics

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Question:

In one state, 52% of the voters are Republicans, and 48% are Democrats. In a second state, 47% of the voters are Republicans, and 53% are Democrats. Suppose a simple random sample of 100 voters are surveyed from each state. What is the probability that the survey will show a greater percentage of Republican voters in the second state than in the first state? (A) 0.04 (B) 0.05 (C) 0.24 (D) 0.71 (E) 0.76

Siqi C.

Answer:

The correct answer is C. For this analysis, let P1 = the proportion of Republican voters in the first state, P2 = the proportion of Republican voters in the second state, p1 = the proportion of Republican voters in the sample from the first state, and p2 = the proportion of Republican voters in the sample from the second state. The number of voters sampled from the first state (n1) = 100, and the number of voters sampled from the second state (n2) = 100. The solution involves four steps. Make sure the sample size is big enough to model differences with a normal population. Because n1P1 = 100 * 0.52 = 52, n1(1 - P1) = 100 * 0.48 = 48, n2P2 = 100 * 0.47 = 47, and n2(1 - P2) = 100 * 0.53 = 53 are each greater than 10, the sample size is large enough. Find the mean of the difference in sample proportions: E(p1 - p2) = P1 - P2 = 0.52 - 0.47 = 0.05. Find the standard deviation of the difference. σd = sqrt{ [ P1(1 - P1) / n1 ] + [ P2(1 - P2) / n2 ] } σd = sqrt{ [ (0.52)(0.48) / 100 ] + [ (0.47)(0.53) / 100 ] } σd = sqrt (0.002496 + 0.002491) = sqrt(0.004987) = 0.0706 Find the probability. This problem requires us to find the probability that p1 is less than p2. This is equivalent to finding the probability that p1 - p2 is less than zero. To find this probability, we need to transform the random variable (p1 - p2) into a z-score. That transformation appears below. z p1 - p2 = (x - μ p1 - p2 ) / σd = = (0 - 0.05)/0.0706 = -0.7082 Using Stat Trek's Normal Distribution Calculator, we find that the probability of a z-score being -0.7082 or less is 0.24. Therefore, the probability that the survey will show a greater percentage of Republican voters in the second state than in the first state is 0.24.

Statistics

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Question:

If you choose an answer at random for a multiple choose question with 4 options , what is the change you will be correct? a. 25% b. 50% c. 60% d.70%

Siqi C.

Answer:

The answer is 25%, because the definition of probability is equal to the number of desired frequency divided by the overall event frequency, that is 1/4 = 25% in this case.

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