Question 1

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.

Accepted Answer

A) 0.25 batters 
B)  0.75 batters 
C)  0.37 batters 
D)  0.32 batters 
E)  0.2 batters

Question 2

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.

Accepted Answer

The answer of If you roll a die 300 times,...

Question 3

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

Accepted Answer

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

Question 4

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

Accepted Answer

The answer of IQ scores (as measured by the Stanford-Binet...

Question 5

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

Accepted Answer

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

Question 6

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.

Accepted Answer

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

Question 7

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.

Accepted Answer

The answer of A roulette wheel has the numbers 1...

Question 8

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

Accepted Answer

A)  $s = 7.21$ 
B)  $s = 0.96$ 
C)  $s = 3.8$ 
D)  $s = 0.92$ 
E)  $s = 14.42$

Question 9

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.

Accepted Answer

A)  $E ( X ) = 26$ 
B)  $E ( X ) = 1.8$ 
C)  $E ( X ) = 3$ 
D)  $E ( X ) = 2.5$ 
E)  $E ( X ) = 3.2$

Question 10

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.

Accepted Answer

A)  0.02304 
B)   0.3456 
C)   0.03456 
D)   0.0008 
E)   0.2304

Question 11

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.
​ $P ( - 2.23 \leq Z \leq 1.43 ) \approx$ __________

Accepted Answer

The answer of Z is the standard normal distribution. Find...

Question 12

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

Accepted Answer

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

Question 13

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.

Accepted Answer

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

Question 14

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

Accepted Answer

The answer of In your bid to be elected class...

Question 15

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

Accepted Answer

A)  $P ( X = 4 ) = 0.13824$ 
B)  $P ( X = 4 ) = 0.4$ 
C)  $P ( X = 4 ) = 0.16667$ 
D)  $P ( X = 4 ) = 0.06144$ 
E)  $P ( X = 4 ) = 0.69984$

Question 16

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. $$\begin{array} { | c | c | c | c | c | c | c | c | c | c | c | } 
\hline x & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \
\hline P ( X = x ) & 0.05 & 0.1 & 0.31 & 0.21 & 0.11 & 0.16 & 0.02 & 0.02 & 0.01 & 0.01 \
\hline
\end{array}$$

Accepted Answer

A) 6 
B)  4 
C)  5 
D)  7 
E)  3

Question 17

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.

Accepted Answer

A)  $\sigma = 1.4$ 
B)  $\sigma = 0.87$ 
C)  $\sigma = 0.75$ 
D)  $\sigma = 0.25$ 
E)  $\sigma = 0.13$

Question 18

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.

Accepted Answer

The answer of The following is a sample of the...

Question 19

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.

Accepted Answer

The answer of Your class is given a mathematics exam...

Question 20

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.

Accepted Answer

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

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: $\begin{array} { c c c c c } x & 10 & 20 & 30 & 40 \\P ( X = x ) & \frac { 25 } { 60 } & \frac { 20 } { 60 } & \frac { 5 } { 60 } & \frac { 10 } { 60 }\end{array}$ $E ( X ) =$ __________

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.

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. $\begin{array} { | c | c | c | c | c | } \hline x & 1 & 2 & 3 & 4 \\\hline P ( X = x ) & 0.1 & 0.4 & 0.2 & 0.3 \\\hline\end{array}$ $\sigma =$ __________

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.

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.

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.

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)≈ __________

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.

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. $P ( - 2.23 \leq Z \leq 1.43 ) \approx$ __________

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.