C

1103134410

Level: 
C
The heights (\(\mathrm{cm}\)) of ten boys and their best performances (\(\mathrm{cm}\)) in standing long jump at the international athletic championship are listed in the following table. Determine the correlation coefficient \( r \) between height of boys and their longest jump. You can use a statistics mode of your calculator to carry out statistical computations. Round the result to four decimal places. Based on the following scatterplot and the correlation coefficient interpret the strength of linear relationship between analysed variables. \[ \begin{array}{|c|c|c|c|c|c|} \hline \textbf{Boy's height (cm)} & 189 & 175 & 187 & 183 & 174 \\\hline \textbf{Length of the jump (cm)} & 231 & 207 & 214 & 223 & 202 \\\hline \\\hline \textbf{Boy's height (cm)} & 193 & 179 & 169 & 186 & 183 \\\hline \textbf{Length of the jump (cm)} & 242 & 229 & 190 & 226 & 212 \\\hline \end{array} \]
strong linear relationship: \( r = 0{.}8628 \)
moderate linear relationship: \( r = 0{.}5542 \)
moderate linear relationship: \( r = 0{.}7444 \)
strong linear relationship: \( r = 0{.}9289 \)

1003134409

Level: 
C
Twenty-five students of the \( 7 \)th grade took an IQ test and SAT Reasoning Test. Results of the tests are denoted by IQ and SQ in headers of the following cross table. In the table the numbers of students are listed according to the results in both tests, while the results of both tests are classified in intervals. Determine the correlation coefficient between IQ and SQ. Round the result to four decimal places. Use your calculator in Statistics mode to carry out statistical calculations. \[ \begin{array}{|c|c|c|c|c|} \hline \textbf{SQ \ IQ} & \mathbf{(85;95]} & \mathbf{(95;105]} & \mathbf{(105;115]} & \mathbf{(115;125]} \\\hline \mathbf{(40;60]} & 1 & & & \\\hline \mathbf{(60;80]} & & 10 & 6 & 1 \\\hline \mathbf{(80;100]} & & & 6 & 1 \\\hline \end{array}\]
\( 0{.}6086 \)
\( 0{.}0086 \)
\( 0{.}9605 \)
\( -0{.}6806 \)

1103134408

Level: 
C
The values of variables \( x \) and \( y \) are listed in the following table and visualized in the next graph. Calculate the correlation coefficient of \( x \) and \( y \) and round it to four decimal places. \[ \begin{array}{|c|c|c|c|c|c|} \hline x & 5 & 6 & 7 & 9 & 11 \\\hline y & 3 & 2 &4 & 6 & 8 \\\hline \end{array} \]
\( 0{.}9569 \)
\( 0{.}9659 \)
\( 0{.}9695 \)
\( 0{.}9596 \)

1003171601

Level: 
C
Consider the function \( f \) given by \( f(x)=\frac12x+\frac32 \) and consider the line \( p \) that is parallel to the \( x \)-axis and intersects \( y \)-axis at the point \( \left[0;\frac12\right] \). Find the function \( g \) such that the graph of \( g \) is symmetric with the graph of \( f \) about the line \( p \).
\( g(x)=-\frac12x-\frac12 \)
\( g(x)=2x-\frac12 \)
\( g(x)=-\frac12x-\frac32 \)
\( g(x)=\frac12x-\frac32 \)

1003158309

Level: 
C
Students of a class take a multiple choice test consisting of \( 10 \) tasks. There are \( 5 \) optional answers to each of the tasks, while only one answer is correct. One student, however, did not study for the test at all. Therefore, he circles his answers randomly, without performing any calculations. Find the probability that he will circle at least \( 3 \) correct answers. Round the result to four decimal places.
\( 0{.}3222 \)
\( 0{.}8591 \)
\( 0{.}1409 \)
\( 0{.}6778 \)

1003158308

Level: 
C
The probability that the randomly selected product is first-class quality is \( 0{.}12 \). Determine the probability that at least \( 2 \) out of \( 50 \) randomly selected products are first-class quality. Round the result to four decimal places.
\( 0{.}9869 \)
\( 0{.}9689 \)
\( 0{.}8969 \)
\( 0{.}8699 \)
\( 0{.}9896 \)
\( 0{.}8996 \)

1003158307

Level: 
C
Suppose that the success rate of one specific medical treatment is \( 90\,\% \). If the treatment is given to \( 20 \) new patients, what is the probability that it is effective in at least \( 18 \) of them? Round the result to four decimal places.
\( 0{.}6769 \)
\( 0{.}9000 \)
\( 0{.}2852 \)
\( 0{.}7148 \)
\( 0{.}8100 \)
Error | math4u.vsb.cz

Error

The website encountered an unexpected error. Please try again later.