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In the distribution of the weights of the fish in a certain sample, a weight of 30 pounds is 2.2 standard deviations above the mean and a weight of 14 pounds is 1.8 standard deviations below the mean. What is the mean of the wveights of the fish in this sample, to the nearest pound?
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?
In a list of numbers, 20.0 is 2 standard deviation above the mean, while 6.5 is 3 standard deviation below the mean.

Quantity A

The average of the list of numbers

Quantity B

14.6


The table above summarizes customer satisfaction ratings for two banks, where each rating is an integer from 1 to 10. Which of the following statements must be true?

Indicate all such statements.


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?
In a normal distribution of data x, the mean is 400, while the standard deviation is 60.

Quantity A

P(400 < x < 430)

Quantity B

P(430 < x < 460)
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.
Let x be a positive number. The random variable R is normally distributed with mean x and standard deviation 0.25x. The random variable T is normally distributed with mean 0.5x and standard deviation 0.5x.

Quantity A

P (R <1.375x)

Quantity B

P (T <1.25x)


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

The random variable Y is normally distributed with mean 576. If the value 628 is at the $$84^{th}$$ percentile of the distribution of Y, which of the following is the best estimate of the value at the $$98^{th}$$ percentile of the distribution of Y?
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 $$−3 \leq x \leq 2$$

Quantity A

The median of the distribution of $$x$$

Quantity B

-$$\frac{9}{5}$$
Sets R, S and T are finite and T contains more elements than S. The number of elements in T minus the number of elements in S is equal to the number of elements in the set R∩T minus the number of elements in the set R∩S.

Quantity A

The number of elements in the set R∪S

Quantity B

The number of elements in the set R∪T
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?
In a group of 100 adults, each owns a DVD player, a CD player, or both. If 60 adults own a DVD player and 70 adults own a CD player, how many adults own both?
In a group of people, 15% have license, 10% have parking tickets, while 78% have neither license nor parking tickets. What percent of people have both license and parking tickets?
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 a survey, employees who want to switch jobs were asked what issues were most important in choosing another job. Half of those surveyed said "salary" and 35% said "location". If 32 percent of those surveyed said both "salary" and "location", what percent said either "salary" or "location" but not both?

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