If we model after-tax household income with a normal distribution, then the figures of a 1995 study imply the information in the following table. Assume that the distribution of incomes in each country is normal, and round all percentages to the nearest whole number. What percentage of Sweden households had an income of $50,000 or more $\begin{array} { | l | l | l | l | l | l | } \hline \text { Country } & \text { U.S. } & \text { Canada } & \text { Switzerland } & \text { Germany } & \text { Sweden } \\ \hline \begin{array} { l } \text { Mean } \\ \text { household } \\ \text { income } \end{array} & \$ 38,000 & \$ 35,000 & \$ 39,000 & \$ 34,000 & \$ 32,000 \\ \hline \begin{array} { l } \text { Standard } \\ \text { deviation } \end{array} & \$ 21,000 & \$ 17,000 & \$ 16,000 & \$ 14,000 & \$ 11,000 \\ \hline \end{array}$

A) 22% B) 95% C) 4% D) 89% E) 5% A) 22% B) 95% C) 4% D) 89% E) 5%

Calculate the expected value of X for the given probability distribution. \[\begin{array} { c c c c c } x & 1 & 2 & 3 & 4 \\ P ( X = x ) & 0.6 & 0.1 & 0.1 & 0.2 \end{array}\]

A) $E ( X ) = 1.6$ B) $E ( X ) = 2.1$ C) $E ( X ) = 2.4$ D) $E ( X ) = 1.9$ E) $E ( X ) = 2.3$ A) $E ( X ) = 1.6$ B) $E ( X ) = 2.1$ C) $E ( X ) = 2.4$ D) $E ( X ) = 1.9$ E) $E ( X ) = 2.3$

A random variable has the probability distribution table as shown. Calculate $P ( x \geq 5 )$ . \[\begin{array} { c | l | l | l | l | l | } \hline x & 1 & 3 & 5 & 7 & 9 \\ \hline P ( X = x ) & 0.4 & 0.2 & 0.1 & & 0.2 \\ \hline \end{array}\] \[P ( x \geq 5 ) =\] __________

The answer of A random variable has the probability distribution...

The following table shows the average percentage increase in the price of a house from 1980 to 2001 in 9 regions of the U.S. $\begin{array} { | l | l | } \hline \text { New England } & 300 \\ \hline \text { Pacific } & 225 \\ \hline \text { Middle Atlantic } & 225 \\ \hline \text { South Atlantic } & 175 \\ \hline \text { Mountain } & 175 \\ \hline \text { West North Central } & 100 \\ \hline \text { West South Central } & 75 \\ \hline \text { East North Central } & 175 \\ \hline \text { East South Central } & 100 \\ \hline \end{array}$ Let X be the percentage increase in the price of a house in a randomly selected region. What is the probability that, in a randomly selected region, the percentage increase in the cost of a house exceeded 200%

A) $P ( X > 200 ) = \frac { 1 } { 9 }$ B) $P ( X > 200 ) = \frac { 2 } { 3 }$ C) $P ( X > 200 ) = \frac { 1 } { 3 }$ D) $P ( X > 200 ) = \frac { 1 } { 2 }$ E) $P ( X > 200 ) = \frac { 2 } { 9 }$ A) $P ( X > 200 ) = \frac { 1 } { 9 }$ B) $P ( X > 200 ) = \frac { 2 } { 3 }$ C) $P ( X > 200 ) = \frac { 1 } { 3 }$ D) $P ( X > 200 ) = \frac { 1 } { 2 }$ E) $P ( X > 200 ) = \frac { 2 } { 9 }$

Find the expected value of the following probability distribution. \[\begin{array} { c c c c c } x & 3 & 9 & 12 & 16 \\ P ( X = x ) & 0.3 & 0.5 & 0.1 & 0.1 \end{array}\]

A) 7.3 B) 4 C) 2.5 D) 8.2 E) 10 A) 7.3 B) 4 C) 2.5 D) 8.2 E) 10

Calculate the standard deviation of X for the probability distribution. \[\begin{array} { | c | c | c | c | c | } \hline x & 1 & 2 & 3 & 4 \\ \hline P ( X = x ) & 0.2 & 0.3 & 0.3 & 0.2 \\ \hline \end{array}\] Round your answer to two decimal places if necessary.

A) 1.05 B) 1 C) 1.02 D) 2.5 E) 5 A) 1.05 B) 1 C) 1.02 D) 2.5 E) 5

Exam 9: Random Variables and Statistics

In a large on-the-job training program, half of the participants are female and half are male. In a random sample of 6 participants, what is the probability that an investigator will draw at least 2 females Round your answer to four decimal places.

(Multiple Choice)

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Question 21

If we model after-tax household income with a normal distribution, then the figures of a 1995 study imply the information in the following table. Assume that the distribution of incomes in each country is normal, and round all percentages to the nearest whole number. What percentage of Sweden households had an income of $50,000 or more Country U.S. Canada Switzerland Germany Sweden Mean household income \ 38,000 \ 35,000 \ 39,000 \ 34,000 \ 32,000 Standard deviation \ 21,000 \ 17,000 \ 16,000 \ 14,000 \ 11,000

(Multiple Choice)

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Question 22

Calculate the expected value of X for the given probability distribution. x 1 2 3 4 P(X=x) 0.6 0.1 0.1 0.2

(Multiple Choice)

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Question 23

Compute the (sample) variance and the standard deviation for the data. $2.1 , - 5.4,4.6,4.1 , - 0.1 , - 0.1$ Please round your answers to two decimal places. $s ^ { 2 } =$ $s =$

(Short Answer)

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Question 24

A random variable has the probability distribution table as shown. Calculate $P ( x \geq 5 )$ . x 1 3 5 7 9 P(X=x) 0.4 0.2 0.1 0.2 $P ( x \geq 5 ) =$ __________

(Short Answer)

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Question 25

Calculate the standard deviation of the given random variable X. Please round your answer to two decimal places. Forty-five darts are thrown at a dartboard. The probability of hitting a bull's-eye is 0.4. Let X be the number of bull's-eyes hit.

(Multiple Choice)

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Question 26

Given the data. $4,0 , - 4,4,6$ Compute the mean.

(Multiple Choice)

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Question 27

You are performing seven independent Bernoulli trials with $p = 0.7$ and $q = 0.3$ . Calculate the probability of two successes. Round your answer to five decimal places if necessary.

(Multiple Choice)

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Question 28

The following is a sample of tow ratings (in pounds) for some popular 2000 model light trucks: 2,000, 2,000, 4,000, 5,000, 6,000, 7,000, 7,000, 7,000, 8,000, 8,000 Compute the mean of the given sample. Round your answer to the nearest whole number. $\bar { x } =$ Compute the standard deviation of the given sample. Round your answer to the nearest whole number. $s =$ Assuming the distribution of tow ratings for all popular light trucks is symmetric and bell-shaped, 68 percent of all light trucks have tow ratings between and . Please, use the rounded value for the standard deviation here. Find the percentage of scores in the sample that fall in this range. __%

(Short Answer)

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Question 29

The probability that a randomly selected pound of beef is purchased by McDonald's is 0.09. Ten pounds of beef are chosen at random. What is the probability that exactly two of them are purchased by McDonald's Round your answer to four decimal places.

(Multiple Choice)

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Question 30

Calculate the standard deviation of X for the probability distribution. Please round your answer to the nearest whole number, if necessary. x -5 -2 0 3 6 9 P(X=x) 0.2 0.3 0.2 0.1 0 0.2 $\sigma =$ __________

(Short Answer)

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Question 31

According to classical mechanics, the energy of an electron in a hydrogen atom can assume any positive value. V - the energy of an electron in a hydrogen atom. Classify the random variable V as finite, discrete infinite, or continuous.

(Short Answer)

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Question 32

If we model after-tax household income by a normal distribution, then the figures of a 1995 study imply the information in the following table. Assume that the distribution of incomes in each country is bell-shaped and symmetric. If we define a "rich" household as one whose after-tax income is at least 1.3 standard deviations above the mean, find the household income of a rich family in Germany. Country U.S. Canada Switzerland Germany Sweden Mean Household Income \ 38,000 \ 35,000 \ 39,000 \ 34,000 \ 32,000 Standard Deviation \ 21,000 \ 17,000 \ 16,000 \ 14,000 \ 11,000 The household income of a rich family in Germany is or (more or less).

(Short Answer)

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Question 33

Calculate the standard deviation of X for the probability distribution. Please round your answer to two decimal places, if necessary. x -5 -2 0 3 6 10 P(X=x) 0.2 0.3 0.2 0.1 0 0.2

(Multiple Choice)

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Question 34

The following table shows the average percentage increase in the price of a house from 1980 to 2001 in 9 regions of the U.S. New England 300 Pacific 225 Middle Atlantic 225 South Atlantic 175 Mountain 175 West North Central 100 West South Central 75 East North Central 175 East South Central 100 Let X be the percentage increase in the price of a house in a randomly selected region. What is the probability that, in a randomly selected region, the percentage increase in the cost of a house exceeded 200%

(Multiple Choice)

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Question 35

You are performing seven independent Bernoulli trials with $p = 0.1$ and $q = 0.9$ . Calculate the probability of no successes. Round your answer to four decimal places.

(Short Answer)

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Question 36

Find the expected value of the following probability distribution. x 3 9 12 16 P(X=x) 0.3 0.5 0.1 0.1

(Multiple Choice)

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Question 37

If we model after-tax household income by a normal distribution, then the figures of a 1995 study imply the information in the following table. Assume that the distribution of incomes in each country is bell-shaped and symmetric. Find the percentage of swiss families which earned an after-tax income of $71,000 or more. Round your answer to one decimal place if necessary. Country U.S. Canada Switzerland Germany Sweden Mean Household Income \ 38,000 \ 35,000 \ 39,000 \ 34,000 \ 32,000 Standard Deviation \ 21,000 \ 17,000 \ 16,000 \ 14,000 \ 11,000 The percentage is __________%.

(Short Answer)

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Question 38

Calculate the standard deviation of X for the probability distribution. x 1 2 3 4 P(X=x) 0.2 0.3 0.3 0.2 Round your answer to two decimal places if necessary.

(Multiple Choice)

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Question 39

The table shows crashworthiness ratings for several categories of motor vehicles. Take X as the crash-test rating of a small car, Y as the crash-test rating for a small SUV, and so on, as shown in the table. Overall Frontal Crash Test Rating Number Tested 3 (Good) (Acceptable) 1 (Marginal) 0 (Poor) Small Cars X 16 1 11 2 2 Small SUVs Y 10 1 4 4 1 Medium SUVs Z 15 3 5 3 4 Passenger Vans U 14 3 0 3 8 Midsize Cars V 16 3 5 0 8 Large Cars W 19 9 5 3 2 Compute the probability distribution for X. x 3 2 1 0 P(X=x)

(Short Answer)

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Question 40

In a large on-the-job training program, half of the participants are female and half are male. In a random sample of 6 participants, what is the probability that an investigator will draw at least 2 females Round your answer to four decimal places.

Calculate the expected value of X for the given probability distribution. x 1 2 3 4 P(X=x) 0.6 0.1 0.1 0.2

Compute the (sample) variance and the standard deviation for the data. $2.1 , - 5.4,4.6,4.1 , - 0.1 , - 0.1$ Please round your answers to two decimal places. $s ^ { 2 } =$ $s =$

A random variable has the probability distribution table as shown. Calculate $P ( x \geq 5 )$ . x 1 3 5 7 9 P(X=x) 0.4 0.2 0.1 0.2 $P ( x \geq 5 ) =$ __________

Calculate the standard deviation of the given random variable X. Please round your answer to two decimal places. Forty-five darts are thrown at a dartboard. The probability of hitting a bull's-eye is 0.4. Let X be the number of bull's-eyes hit.

Given the data. $4,0 , - 4,4,6$ Compute the mean.

You are performing seven independent Bernoulli trials with $p = 0.7$ and $q = 0.3$ . Calculate the probability of two successes. Round your answer to five decimal places if necessary.

The probability that a randomly selected pound of beef is purchased by McDonald's is 0.09. Ten pounds of beef are chosen at random. What is the probability that exactly two of them are purchased by McDonald's Round your answer to four decimal places.

Calculate the standard deviation of X for the probability distribution. Please round your answer to the nearest whole number, if necessary. x -5 -2 0 3 6 9 P(X=x) 0.2 0.3 0.2 0.1 0 0.2 $\sigma =$ __________

According to classical mechanics, the energy of an electron in a hydrogen atom can assume any positive value. V - the energy of an electron in a hydrogen atom. Classify the random variable V as finite, discrete infinite, or continuous.

Calculate the standard deviation of X for the probability distribution. Please round your answer to two decimal places, if necessary. x -5 -2 0 3 6 10 P(X=x) 0.2 0.3 0.2 0.1 0 0.2

You are performing seven independent Bernoulli trials with $p = 0.1$ and $q = 0.9$ . Calculate the probability of no successes. Round your answer to four decimal places.

Find the expected value of the following probability distribution. x 3 9 12 16 P(X=x) 0.3 0.5 0.1 0.1

Calculate the standard deviation of X for the probability distribution. x 1 2 3 4 P(X=x) 0.2 0.3 0.3 0.2 Round your answer to two decimal places if necessary.

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Introduction to the Derivative

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Exam 9: Random Variables and Statistics

In a large on-the-job training program, half of the participants are female and half are male. In a random sample of 6 participants, what is the probability that an investigator will draw at least 2 females Round your answer to four decimal places.

Calculate the expected value of X for the given probability distribution. x 1 2 3 4 P(X=x) 0.6 0.1 0.1 0.2

Compute the (sample) variance and the standard deviation for the data. ​ 2.1,−5.4,4.6,4.1,−0.1,−0.12.1 , - 5.4,4.6,4.1 , - 0.1 , - 0.12.1,−5.4,4.6,4.1,−0.1,−0.1 ​ Please round your answers to two decimal places. ​ s2=s ^ { 2 } =s2= __________ ​ s=s =s= __________

A random variable has the probability distribution table as shown. Calculate P(x≥5)P ( x \geq 5 )P(x≥5) . x 1 3 5 7 9 P(X=x) 0.4 0.2 0.1 0.2 ​ P(x≥5)=P ( x \geq 5 ) =P(x≥5)= __________

Calculate the standard deviation of the given random variable X. Please round your answer to two decimal places. Forty-five darts are thrown at a dartboard. The probability of hitting a bull's-eye is 0.4. Let X be the number of bull's-eyes hit.

Given the data. 4,0,−4,4,64,0 , - 4,4,64,0,−4,4,6 Compute the mean.

You are performing seven independent Bernoulli trials with p=0.7p = 0.7p=0.7 and q=0.3q = 0.3q=0.3 . Calculate the probability of two successes. Round your answer to five decimal places if necessary.

The probability that a randomly selected pound of beef is purchased by McDonald's is 0.09. Ten pounds of beef are chosen at random. What is the probability that exactly two of them are purchased by McDonald's Round your answer to four decimal places.

Calculate the standard deviation of X for the probability distribution. Please round your answer to the nearest whole number, if necessary. x -5 -2 0 3 6 9 P(X=x) 0.2 0.3 0.2 0.1 0 0.2 ​ σ=\sigma =σ= __________

According to classical mechanics, the energy of an electron in a hydrogen atom can assume any positive value. ​V - the energy of an electron in a hydrogen atom. ​ Classify the random variable V as finite, discrete infinite, or continuous.

Calculate the standard deviation of X for the probability distribution. Please round your answer to two decimal places, if necessary. x -5 -2 0 3 6 10 P(X=x) 0.2 0.3 0.2 0.1 0 0.2

You are performing seven independent Bernoulli trials with p=0.1p = 0.1p=0.1 and q=0.9q = 0.9q=0.9 . Calculate the probability of no successes. Round your answer to four decimal places.

Find the expected value of the following probability distribution. x 3 9 12 16 P(X=x) 0.3 0.5 0.1 0.1

Calculate the standard deviation of X for the probability distribution. x 1 2 3 4 P(X=x) 0.2 0.3 0.3 0.2 Round your answer to two decimal places if necessary.

Functions and Applications

Nonlinear Functions and Models

The Mathematics of Finance

Systems of Linear Equations and Matrices

Matrix Algebra and Applications

Linear Programming

Sets and Counting

Probability

Introduction to the Derivative

Techniques of Differentiation

Applications of the Derivative

The Integral

Further Integration Techniques and Applications of the Integral

Functions of Several Variables

Trigonometric Models

Filters

Compute the (sample) variance and the standard deviation for the data. $2.1 , - 5.4,4.6,4.1 , - 0.1 , - 0.1$ Please round your answers to two decimal places. $s ^ { 2 } =$ $s =$

A random variable has the probability distribution table as shown. Calculate $P ( x \geq 5 )$ . x 1 3 5 7 9 P(X=x) 0.4 0.2 0.1 0.2 $P ( x \geq 5 ) =$ __________

Given the data. $4,0 , - 4,4,6$ Compute the mean.

You are performing seven independent Bernoulli trials with $p = 0.7$ and $q = 0.3$ . Calculate the probability of two successes. Round your answer to five decimal places if necessary.

Calculate the standard deviation of X for the probability distribution. Please round your answer to the nearest whole number, if necessary. x -5 -2 0 3 6 9 P(X=x) 0.2 0.3 0.2 0.1 0 0.2 $\sigma =$ __________

According to classical mechanics, the energy of an electron in a hydrogen atom can assume any positive value. V - the energy of an electron in a hydrogen atom. Classify the random variable V as finite, discrete infinite, or continuous.

You are performing seven independent Bernoulli trials with $p = 0.1$ and $q = 0.9$ . Calculate the probability of no successes. Round your answer to four decimal places.