Find the expected value of a random variable X having the following probability distribution: \[\begin{array} { c c c c c } x & 10 & 20 & 30 & 40 \\ P ( X = x ) & \frac { 25 } { 60 } & \frac { 20 } { 60 } & \frac { 5 } { 60 } & \frac { 10 } { 60 } \end{array}\] \[E ( X ) =\] __________

The answer of Find the expected value of a random...

A random variable has the probability distribution table as shown. Calculate \[P ( x \leq - 1 )\] . \[\begin{array} { | l | l | l | l | l | l | } \hline \boldsymbol { x } & - 3 & - 2 & - 1 & 0 & 1 \\ \hline \boldsymbol { P } ( \boldsymbol { X } = \boldsymbol { x } ) & & & 0.5 & 0.1 & 0.1 \\ \hline \end{array}\]

A) 0.5 B) 0.3 C) 0.8 D) 0 E) Cannot be determined from given information. A) 0.5 B) 0.3 C) 0.8 D) 0 E) Cannot be determined from given information.

Calculate the expected value of X for the given probability distribution: \[\begin{array} { c c c c c c c } x & - 20 & - 10 & 0 & 10 & 20 & 30 \\ P ( X = x ) & 0.1 & 0.1 & 0.1 & 0.1 & 0.1 & 0.5 \end{array}\] Round your answer to two decimal places if necessary.

A) $E ( X ) = 14.79$ B) $E ( X ) = 14.87$ C) $E ( X ) = 14$ D) $E ( X ) = 15.1$ E) $E ( X ) = 15$ A) $E ( X ) = 14.79$ B) $E ( X ) = 14.87$ C) $E ( X ) = 14$ D) $E ( X ) = 15.1$ E) $E ( X ) = 15$

Calculate the standard deviation of X for the probability distribution. Round your answer to the whole number. \[\begin{array} { | c | c | c | c | c | } \hline x & 1 & 2 & 3 & 4 \\ \hline P ( X = x ) & 0.1 & 0.4 & 0.2 & 0.3 \\ \hline \end{array}\] \[\sigma =\] __________

The answer of Calculate the standard deviation of X for...

Calculate the standard deviation of X for the probability distribution. \[\begin{array} { | c | c | c | c | c | } \hline x & 2 & 4 & 5 & 3 \\ \hline P ( X = x ) & 0.5 & 0.1 & 0.2 & 0.2 \\ \hline \end{array}\] Round your answer to two decimal places if necessary.

A) 1.25 B) 3 C) 1.4 D) 6 E) 1.18 A) 1.25 B) 3 C) 1.4 D) 6 E) 1.18

Your scores for the 20 surprise math quizzes last semester were (out of 10) $\begin{array} { l l l l l l l l l l l } 5.5&9.5&10.0&2.5&8.0&9.5&7.5&6.5&7.0&8.0\\ 8.0&8.5&7.5&7.0&8.0&10.0&10.0&8.5&7.5&8.0 \end{array}$ Use these raw data to construct a frequency table with the following brackets: 2.1 - 4.0, 4.1 - 6.0, 6.1 - 8.0, 8.1 - 10.0. Find the probability distribution using the (rounded) midpoint values as the values of X.

A) $\begin{array} { l } x & 3.0&5.0&7.0&9.0\\ P ( X = x ) &0.05&0.55&0.05&0.35 \\ \end{array}$ B) $\begin{array} { l } x & 3.0&5.0&7.0&9.0\\ P ( X = x ) &0.05&0.05&0.55&0.35 \\ \end{array}$ C) $\begin{array} { l } x & 3.0&5.0&7.0&9.0\\ P ( X = x ) &0.05&0.55&0.35&0.05 \\ \end{array}$ D) $\begin{array} { l } x & 3.0&5.0&7.0&9.0\\ P ( X = x ) &0.35&0.55&0.05&0.05 \\ \end{array}$ E) $\begin{array} { l } x & 3.0&5.0&7.0&9.0\\ P ( X = x ) &0.05&0.05&0.55&0.35 \\ \end{array}$. A) $\begin{array} { l } x & 3.0&5.0&7.0&9.0\\ P ( X = x ) &0.05&0.55&0.05&0.35 \\ \end{array}$ B) $\begin{array} { l } x & 3.0&5.0&7.0&9.0\\ P ( X = x ) &0.05&0.05&0.55&0.35 \\ \end{array}$ C) $\begin{array} { l } x & 3.0&5.0&7.0&9.0\\ P ( X = x ) &0.05&0.55&0.35&0.05 \\ \end{array}$ D) $\begin{array} { l } x & 3.0&5.0&7.0&9.0\\ P ( X = x ) &0.35&0.55&0.05&0.05 \\ \end{array}$ E) $\begin{array} { l } x & 3.0&5.0&7.0&9.0\\ P ( X = x ) &0.05&0.05&0.55&0.35 \\ \end{array}$.

Exam 9: Random Variables and Statistics

The mean batting average in major league baseball is about 0.250. Supposing that batting averages are normally distributed, that the standard deviation in the averages is 0.05, and that there are 245 batters, what is the expected number of batters with an average of at least 0.400 Round your answer to two decimal places.

(Multiple Choice)

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Question 61

If you roll a die 300 times, what is the probability that you will roll between 50 and 80 sixs Please, round your answer to three decimal places.

(Short Answer)

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Question 62

Find the expected value of a random variable X having the following probability distribution: x 10 20 30 40 P(X=x) $E ( X ) =$ __________

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Question 63

IQ scores (as measured by the Stanford-Binet intelligence test) are normally distributed with a mean of 100 and a standard deviation of 16. Find the approximate number of people in the U.S. (assuming a total population of 280,000,000) with an IQ higher than 120. Round your answer to the nearest 100,000. __________ people

(Short Answer)

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Question 64

A random variable has the probability distribution table as shown. Calculate $P ( x \leq - 1 )$ . -3 -2 -1 0 1 ( = ) 0.5 0.1 0.1

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Question 65

Calculate the expected value of X for the given probability distribution: x -20 -10 0 10 20 30 P(X=x) 0.1 0.1 0.1 0.1 0.1 0.5 Round your answer to two decimal places if necessary.

(Multiple Choice)

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Question 66

A roulette wheel has the numbers 1 through 36, 0, and 00. A bet on two numbers pays 17 to 1 (that is, if one of the two numbers you bet comes up, you get back your $1 plus another $17). How much do you expect to win with a $8 bet on two numbers Please, round your answer to the nearest thousandth of a dollar. You expect to (win or lose) $ on each spin of the wheel.

(Short Answer)

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Question 67

Compute the (sample) standard deviation for the data. Please round your answer to two decimal places. $2.8 , - 5.6,4.4,4.3 , - 0.2 , - 0.2$

(Multiple Choice)

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Question 68

Select five cards without replacement from a standard deck of 52, and let X be the number of black cards you draw. Calculate the expected value of the given random variable X.

(Multiple Choice)

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Question 69

Consider a Bernoulli experiment with $n = 5$ and $p = 0.4$ . What is $P ( X = 3 )$ ? Round your answer to five decimal places if necessary.

(Multiple Choice)

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Question 70

Z is the standard normal distribution. Find the probability $P ( - 2.23 \leq Z \leq 1.43 )$ . Please, round your answer to three decimal places. $P ( - 2.23 \leq Z \leq 1.43 ) \approx$ __________

(Short Answer)

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Question 71

Calculate the standard deviation of X for the probability distribution. Round your answer to the whole number. x 1 2 3 4 P(X=x) 0.1 0.4 0.2 0.3 $\sigma =$ __________

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Question 72

Calculate the standard deviation of X for the probability distribution. x 2 4 5 3 P(X=x) 0.5 0.1 0.2 0.2 Round your answer to two decimal places if necessary.

(Multiple Choice)

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Question 73

In your bid to be elected class representative, you have your election committee survey five randomly chosen students in your class and ask them to rank you on a scale of 0 - 10. Your rankings are 6, 2, 7, 4, 8. (a) Find the sample mean, rounded to two decimal places. $\bar { x } =$ (b) Calculate the sample standard deviation, rounded to two decimal places. $5 \approx$ (c) Assuming the sample mean and standard deviation are indicative of the class as a whole, in what range does the empirical rule predict that approximately 68% of the class will rank you

(Short Answer)

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Question 74

X is a binomial variable with $n = 6$ and $p = 0.4$ . Compute $P ( X = 4 )$ . Round your answer to five decimal places.

(Multiple Choice)

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Question 75

Your company, Sonic Video, Inc., has conducted research that shows the following probability distribution, where X is the number of video arcades in a randomly chosen city with more than 500,000 inhabitants. As CEO of Startrooper Video Unlimited, you wish to install a chain of video arcades in Sleepy City, U.S.A. The city council regulations require that the number of arcades be within the range shared by at least 75 percent of all cities. Find the largest number of video arcades you should install so as to comply with this regulation. x 0 1 2 3 4 5 6 7 8 9 P(X=x) 0.05 0.1 0.31 0.21 0.11 0.16 0.02 0.02 0.01 0.01

(Multiple Choice)

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Question 76

Calculate the standard deviation of the given random variable X. Please, round your answer to two decimal places, if necessary. X is the number of heads that come up when a coin is tossed three times.

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Question 77

The following is a sample of the percentage increases in the price of a house from 1980 to 2001 in 8 regions of the U.S. 80, 125, 145, 155, 155, 220, 220, 300 Compute the mean of the given sample. $\bar { x } =$ Compute the median of the given sample. $m =$ Fill in the blank: As many regions in the U.S. had housing increases averaging more than __% as below that.

(Short Answer)

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Question 78

Your class is given a mathematics exam worth 50 points; X is the average score, rounded to the nearest whole number. Classify the random variable X as finite, discrete infinite, or continuous.

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Question 79

Your scores for the 20 surprise math quizzes last semester were (out of 10) 5.5 9.5 10.0 2.5 8.0 9.5 7.5 6.5 7.0 8.0 8.0 8.5 7.5 7.0 8.0 10.0 10.0 8.5 7.5 8.0 Use these raw data to construct a frequency table with the following brackets: 2.1 - 4.0, 4.1 - 6.0, 6.1 - 8.0, 8.1 - 10.0. Find the probability distribution using the (rounded) midpoint values as the values of X.

(Multiple Choice)

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Question 80

If you roll a die 300 times, what is the probability that you will roll between 50 and 80 sixs Please, round your answer to three decimal places.

Find the expected value of a random variable X having the following probability distribution: x 10 20 30 40 P(X=x) $E ( X ) =$ __________

A random variable has the probability distribution table as shown. Calculate $P ( x \leq - 1 )$ . -3 -2 -1 0 1 ( = ) 0.5 0.1 0.1

Calculate the expected value of X for the given probability distribution: x -20 -10 0 10 20 30 P(X=x) 0.1 0.1 0.1 0.1 0.1 0.5 Round your answer to two decimal places if necessary.

Compute the (sample) standard deviation for the data. Please round your answer to two decimal places. $2.8 , - 5.6,4.4,4.3 , - 0.2 , - 0.2$

Select five cards without replacement from a standard deck of 52, and let X be the number of black cards you draw. Calculate the expected value of the given random variable X.

Consider a Bernoulli experiment with $n = 5$ and $p = 0.4$ . What is $P ( X = 3 )$ ? Round your answer to five decimal places if necessary.

Z is the standard normal distribution. Find the probability $P ( - 2.23 \leq Z \leq 1.43 )$ . Please, round your answer to three decimal places. $P ( - 2.23 \leq Z \leq 1.43 ) \approx$ __________

Calculate the standard deviation of X for the probability distribution. Round your answer to the whole number. x 1 2 3 4 P(X=x) 0.1 0.4 0.2 0.3 $\sigma =$ __________

Calculate the standard deviation of X for the probability distribution. x 2 4 5 3 P(X=x) 0.5 0.1 0.2 0.2 Round your answer to two decimal places if necessary.

X is a binomial variable with $n = 6$ and $p = 0.4$ . Compute $P ( X = 4 )$ . Round your answer to five decimal places.

Calculate the standard deviation of the given random variable X. Please, round your answer to two decimal places, if necessary. X is the number of heads that come up when a coin is tossed three times.

Your class is given a mathematics exam worth 50 points; X is the average score, rounded to the nearest whole number. Classify the random variable X as finite, discrete infinite, or continuous.

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Matrix Algebra and Applications

Linear Programming

Sets and Counting

Probability

Introduction to the Derivative

Techniques of Differentiation

Applications of the Derivative

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Further Integration Techniques and Applications of the Integral

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Exam 9: Random Variables and Statistics

If you roll a die 300 times, what is the probability that you will roll between 50 and 80 sixs Please, round your answer to three decimal places.

Find the expected value of a random variable X having the following probability distribution: x 10 20 30 40 P(X=x) ​ E(X)=E ( X ) =E(X)= __________

A random variable has the probability distribution table as shown. Calculate P(x≤−1)P ( x \leq - 1 )P(x≤−1) . -3 -2 -1 0 1 ( = ) 0.5 0.1 0.1

Calculate the expected value of X for the given probability distribution: x -20 -10 0 10 20 30 P(X=x) 0.1 0.1 0.1 0.1 0.1 0.5 Round your answer to two decimal places if necessary.

Compute the (sample) standard deviation for the data. Please round your answer to two decimal places. 2.8,−5.6,4.4,4.3,−0.2,−0.22.8 , - 5.6,4.4,4.3 , - 0.2 , - 0.22.8,−5.6,4.4,4.3,−0.2,−0.2

Select five cards without replacement from a standard deck of 52, and let X be the number of black cards you draw. Calculate the expected value of the given random variable X.

Consider a Bernoulli experiment with n=5n = 5n=5 and p=0.4p = 0.4p=0.4 . What is P(X=3)P ( X = 3 )P(X=3) ? Round your answer to five decimal places if necessary.

Z is the standard normal distribution. Find the probability P(−2.23≤Z≤1.43)P ( - 2.23 \leq Z \leq 1.43 )P(−2.23≤Z≤1.43) . Please, round your answer to three decimal places. ​ P(−2.23≤Z≤1.43)≈P ( - 2.23 \leq Z \leq 1.43 ) \approxP(−2.23≤Z≤1.43)≈ __________

Calculate the standard deviation of X for the probability distribution. Round your answer to the whole number. x 1 2 3 4 P(X=x) 0.1 0.4 0.2 0.3 ​ σ=\sigma =σ= __________

Calculate the standard deviation of X for the probability distribution. x 2 4 5 3 P(X=x) 0.5 0.1 0.2 0.2 Round your answer to two decimal places if necessary.

X is a binomial variable with n=6n = 6n=6 and p=0.4p = 0.4p=0.4 . Compute P(X=4)P ( X = 4 )P(X=4) . Round your answer to five decimal places.

Calculate the standard deviation of the given random variable X. Please, round your answer to two decimal places, if necessary. X is the number of heads that come up when a coin is tossed three times.

Your class is given a mathematics exam worth 50 points; X is the average score, rounded to the nearest whole number. ​ Classify the random variable X as finite, discrete infinite, or continuous.

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

Find the expected value of a random variable X having the following probability distribution: x 10 20 30 40 P(X=x) $E ( X ) =$ __________

A random variable has the probability distribution table as shown. Calculate $P ( x \leq - 1 )$ . -3 -2 -1 0 1 ( = ) 0.5 0.1 0.1

Compute the (sample) standard deviation for the data. Please round your answer to two decimal places. $2.8 , - 5.6,4.4,4.3 , - 0.2 , - 0.2$

Consider a Bernoulli experiment with $n = 5$ and $p = 0.4$ . What is $P ( X = 3 )$ ? Round your answer to five decimal places if necessary.

Z is the standard normal distribution. Find the probability $P ( - 2.23 \leq Z \leq 1.43 )$ . Please, round your answer to three decimal places. $P ( - 2.23 \leq Z \leq 1.43 ) \approx$ __________

Calculate the standard deviation of X for the probability distribution. Round your answer to the whole number. x 1 2 3 4 P(X=x) 0.1 0.4 0.2 0.3 $\sigma =$ __________

X is a binomial variable with $n = 6$ and $p = 0.4$ . Compute $P ( X = 4 )$ . Round your answer to five decimal places.

Your class is given a mathematics exam worth 50 points; X is the average score, rounded to the nearest whole number. Classify the random variable X as finite, discrete infinite, or continuous.