# Tutor profile: Siqi C.

## Questions

### Subject: GRE

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

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

### Subject: Statistics

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

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.

### Subject: Statistics

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%

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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