GRE考满分·题库

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题目内容
In the distribution of measurements of the variable x, the mean is 56 and the measurement r lies between the 65th and 70th percentiles. In the distribution of measurements of the variable y, the mean is 56 and the measurement t lies between the 75th and 80th percentiles.

Quantity A

r

Quantity B

t
Larry and Tony work for different companies. Larry`s salary is the $$90^{th}$$ percentile of the salaries in his company, and Tony`s salary is the $$70^{th}$$ percentile of the salaries in his company.

Which of the following statements individually provide(s) sufficient additional information to conclude that Larry`s salary is higher than Tony`s salary?

Indicate all such statements.


The table shows the means and ranges of two data sets, X and Y, each containing the same number of measurements.

Quantity A

The standard deviation of data set X

Quantity B

The standard deviation of data set Y

Quantity A

The standard deviation of the numbers 45, 64, 83, and 53

Quantity B

The standard deviation of the numbers 55, 81, 47, and 62
For a certain normal distribution, the value 15.6 is 2 standard deviations below the mean of the distribution and the value 26.1 is 3 standard deviations above the mean of the distribution. What is the mean of the distribution?


The random variable X has the standard normal distribution with a mean of 0 and a standard deviation of 1, as shown. Probabilities, rounded to the nearest 0.01, are indicated for the six intervals shown. The random variable Y has a normal distribution with a mean of 2 and a standard deviation of 1. Using the probabilities shown, approximately how much greater is the probability that the value of Y is between 1 and 2 than the probability that the value of X is between 1 and 2?
For a certain normal distribution, its mean and standard deviation are 50 and 5.4, respectively.

Quantity A

The number of data in (45, 48.6)

Quantity B

The number of data in (55.4, 59)
Data set A and B are both normally distributed. In data set A, the mean is 60, standard deviation is 9, and 72 is $$q$$th percentile. In data set B, the mean is 70, standard deviation is 6, and 78 is $$w$$th percentile.

Quantity A

q

Quantity B

w


The figure above shows a normal distribution with mean m and standard deviation d, including approximate percents of the distribution corresponding to the six regions shown.

The lengths of phone calls made on a certain weekend by students at High School H are approximately normally distributed with a mean of 30 minutes and a standard deviation of 10 minutes. Which of the following statements must be true?

Indicate all such statements.
A normal distribution with mean 50, $$16^{th}$$ percentile: 42,$$33^{th}$$ percentile: q.

Quantity A

q-42

Quantity B

50-q
Let W be a continuous random variable such that P (W > $$\frac{1}{2}$$)=$$\frac{9}{10}$$ and P (W > $$\frac{3}{4}$$)=$$\frac{7}{20}$$. What is the value of P ($$\frac{1}{2}$$ < W ≤ $$\frac{3}{4}$$)?

Give your answer as a fraction.
The probability distribution function f of a continuous random variable x is defined by f(x) = ($$\frac{2}{13}$$)*|x| for −3 ≤ x ≤ 2

Quantity A

The median of the distribution of X

Quantity B

-$$\frac{9}{5}$$
Let S and T be two sets such that the ratio of the number of elements in S to the number of elements in T to the number of elements in the set S∩T is 4 to 3 to 1. If the sum of the number of elements in S but not in T and the number of elements in T but not in S is 2520, what is the number of elements in S∩T?
Among 25 parents, 14 have at least 1 boy, 15 have at least 1 girl

Quantity A

The number of parents who have at least 1 boy but no girl

Quantity B

10
In an election, voters can vote for as many candidates as they wish. The percent of votes each candidate wins is listed as follows.



Quantity A

The percentage of votes candidate A or candidate B or both of them win

Quantity B

80%
In a sequence, each term is equal the preceding term plus a constant x, a5 = 11, a8 = 19, what is the value of x?

Give your answer as a fraction.
In a sequence of numbers 1, 2, 2, 3, 3, 3, 4, 4, 4, 4 ......., n occurs n times for 1 ≤ n ≤ 25. For the first 300 numbers in the sequence, what is the least n that is greater than at least 25% of the first 300 numbers in the sequence?
$$a_k$$ = ($$\frac{1}{k} - \frac{1}{k+1}$$) for any positive integer k.

Quantity A

$$a_3$$+$$a_4$$+$$a_5$$+$$a_6$$+$$a_7$$

Quantity B

$$\frac{1}{8}$$
$$a_1$$=4, $$a_2$$=-3, $$a_3$$=7. If for any integer n greater than 3, $$a_n$$=$$|a_{n-1}-a_{n-2}|$$, then what`s the sum of all the terms from $$a_1$$ to $$a_{35}$$?
There are 2 different choices of Product A, 4 different choices of Product B and 5 different choices of Product C. In how many ways can these products be selected if either 1 or none of item is selected out of Product A, B, and C, respectively?

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