Chapter 12

For each situation, describe a trial and a success. Then design and run a simulation to find the probability. On a true-or-false test, you guess the answers to five questions. Find the probability of guesing the correct answers to exactly three of the five questions.

For each sample, find the sample proportion. Write it as a percent. 837 out of 1150 insurance applicants have no citations on their driving record.

Find the mean, median, and mode of each set of values. $$ \begin{array}{llllllllll}{5} & {9} & {1} & {2} & {7} & {3} & {1} & {8} & {8} & {1} & {3}\end{array} $$

For each situation, describe a trial and a success. Then design and run a simulation to find the probability. A poll shows that 40\(\%\) of the voters in a city favor passage of a bond issue to finance park improvements. If ten voters are selected at random, find the probability that exactly four of them will vote in favor of it.

Find the range and the interquartile range of each set of values. $$ \begin{array}{llllllll}{56} & {78} & {125} & {34} & {67} & {91} & {20}\end{array} $$

For each sample, find the sample proportion. Write it as a percent. 27 out of 60 shoppers prefer generic brands when available.

Find the mean, median, and mode of each set of values. $$ 307 \quad 309 \quad 323 \quad 304 \quad 390 \quad 398 $$

For each situation, describe a trial and a success. Then design and run a simulation to find the probability. A plant production line has a 90\(\%\) probability of not experiencing a breakdown during an eight-hour shift. Find the probability that three successive shifts will not have a breakdown.

Find the range and the interquartile range of each set of values. $$ 724 \quad 786 \quad 670 \quad 760 \quad 300 \quad 187 \quad 190 \quad 345 \quad 456 \quad 732 \quad 891 \quad 879 \quad 324 $$

Find the mean, median, and mode of each set of values. 475 \(\quad\) 722 \(\quad\) 499\(\quad 572 \quad 402 \quad 809 \quad 499 \quad 828 \quad 405 \quad 499 \quad 800 \quad 422 \quad\) 672\(\quad\) 800

For each sample, find the sample proportion. Write it as a percent. 532 out of 580 households own a color television set.

The table shows the frequency of responses to editorials. Find each probability. $$ \begin{array}{|l|l|l|l|l|l|l|}\hline \text { Number of Responses } & {0} & {1} & {2} & {3} & {4} & {5} & {6 \text { or more }} & {\text { Total }} \\ \hline \text { Number of Editorials } & {20} & {30} & {56} & {38} & {34} & {16} & {6} & {200} \\ \hline\end{array} $$ \(P(5 \text { or more responses })\)

Suppose you guess on a true-or-false test. Use a tree diagram to find each probability. \(P(4 \text { correct in } 4 \text { guesses })\)

Find the mean and the standard deviation for each set of values. $$ 7890456 \quad 673 \quad 111 \quad 381 \quad 21 $$

Make a box-and-whisker plot for each set of values. $$ \begin{array}{llllllll}{12} & {11} & {15} & {12} & {19} & {20} & {19}\end{array} $$

The table shows the frequency of responses to editorials. Find each probability. $$ \begin{array}{|l|l|l|l|l|l|l|}\hline \text { Number of Responses } & {0} & {1} & {2} & {3} & {4} & {5} & {6 \text { or more }} & {\text { Total }} \\ \hline \text { Number of Editorials } & {20} & {30} & {56} & {38} & {34} & {16} & {6} & {200} \\ \hline\end{array} $$ \(P(\text { at most } 4 \text { responses })\)

Sketch a normal curve for each distribution. Label the \(x\) -axis values at one, two, and three standard deviations from the mean. mean \(=45,\) standard deviation \(=5\)

Suppose you guess on a true-or-false test. Use a tree diagram to find each probability. \(P(1 \text { correct in } 4 \text { guesses })\)

Find the mean and the standard deviation for each set of values. $$ \begin{array}{llllllll}{13} & {15} & {17} & {18} & {12} & {21} & {10}\end{array} $$

Make a box-and-whisker plot for each set of values. $$ 120 \quad 145 \quad 133 \quad 105 \quad 117 \quad 150 $$

Identify any bias in each sampling method. A maintenance crew wants to estimate how many of 3000 air filters in an office building need replacing. The crew examines five filters chosen at random on each floor of the building.

The table shows the frequency of responses to editorials. Find each probability. $$ \begin{array}{|l|l|l|l|l|l|l|}\hline \text { Number of Responses } & {0} & {1} & {2} & {3} & {4} & {5} & {6 \text { or more }} & {\text { Total }} \\ \hline \text { Number of Editorials } & {20} & {30} & {56} & {38} & {34} & {16} & {6} & {200} \\ \hline\end{array} $$ \(P(0-2 \text { responses })\)

Sketch a normal curve for each distribution. Label the \(x\) -axis values at one, two, and three standard deviations from the mean. mean \(=45,\) standard deviation \(=10\)

Suppose you guess on a true-or-false test. Use a tree diagram to find each probability. \(P(3 \text { correct in } 4 \text { guesses })\)

Make a box-and-whisker plot for each set of values. $$ \begin{array}{llllllll}{49} & {57.5} & {58} & {49.2} & {62} & {22.2} & {67} & {52.1} & {77} & {99.9} & {80} & {51.7} & {64}\end{array} $$

Identify any bias in each sampling method. The student government wants to find out how many students have after-school jobs. A pollster interviews students selected at random as they board buses at the end of the school day.

Sketch a normal curve for each distribution. Label the \(x\) -axis values at one, two, and three standard deviations from the mean. mean \(=45,\) standard deviation \(=2\)

Sketch a normal curve for each distribution. Label the \(x\) -axis values at one, two, and three standard deviations from the mean. mean \(=45,\) standard deviation \(=3.5\)

Find the probability of \(x\) successes in \(n\) trials for the given probability of success \(p\) on each trial. $$ x=3, n=8, p=0.3 $$

Determine the whole number of standard deviations that includes all data values. The mean price of the nonfiction books on a best-sellers list is \(\$ 25.07 ;\) the standard deviation is \(\$ 2.62 .\) \(\$ 26.95, \$ 22.95, \$ 24.00, \$ 24.95, \$ 29.95, \$ 19.95, \$ 24.95, \$ 24.00, \$ 27.95, \$ 25.00\)

Find the values at the 30 th and 90 th percentiles for each set of values. \(\begin{array}{llll}{6283} & {5700} & {6381} & {6274} & {6075} & {5993} & {5581}\end{array}\)

Suppose you roll two number cubes. Graph the probability distribution for each sample space. {sum of numbers even, sum of numbers odd}

A set of data with a mean of 62 and a standard deviation of 5.7 is normally distributed. Find each value, given its distance from the mean. \(+3\) standard deviations

Find the probability of \(x\) successes in \(n\) trials for the given probability of success \(p\) on each trial. $$ x=4, n=8, p=0.3 $$

Find the values at the 30 th and 90 th percentiles for each set of values. \(\begin{array}{lllllllll}{7} & {12} & {3} & {14} & {17} & {20} & {5} & {3} & {17} & {4} & {13} & {2} & {15} & {9} & {15} & {18} & {16} & {9} & {1} & {6}\end{array}\)

Suppose you roll two number cubes. Graph the probability distribution for each sample space. {both numbers even, both numbers odd, one number even and the other odd}

A set of data with a mean of 62 and a standard deviation of 5.7 is normally distributed. Find each value, given its distance from the mean. \(-1\) standard deviation

A data set has mean 25 and standard deviation \(5 .\) Find the \(z\) -score of each value. $$ 39 $$

Find the probability of \(x\) successes in \(n\) trials for the given probability of success \(p\) on each trial. $$ x=5, n=10, p=0.5 $$

Identify the outlier of each set of values. $$ \begin{array}{lllllllll}{3.4} & {4.5} & {2.3} & {5.9} & {9.8} & {3.3} & {2.1} & {3.0} & {2.9}\end{array} $$

A set of data has a normal distribution with a mean of 50 and a standard deviation of \(8 .\) Find the percent of data within each interval. from 42 to 58

A data set has mean 25 and standard deviation \(5 .\) Find the \(z\) -score of each value. $$ 18 $$

Find the probability of \(x\) successes in \(n\) trials for the given probability of success \(p\) on each trial. $$ x=5, n=10, p=0.1 $$

Identify the outlier of each set of values. $$\begin{array}{llllllllll}17 & 21 & 19 & 10 & 15 & 19 & 14 & 0 & 11 & 16\end{array}$$

Make a tree diagram based on the survey results below. Then find \(P(\text { a female }\) respondent is left-handed) and \(P(\text { a respondent is both male and right-handed). }\) \(\bullet\) Of all the respondents, 17\(\%\) are male. \(\bullet\) Of the male respondents, 33\(\%\) are left-handed. \(\bullet\) Of female respondents, 90\(\%\) are right-handed.

A set of data has a normal distribution with a mean of 50 and a standard deviation of \(8 .\) Find the percent of data within each interval. greater than 34

A football team has a 70\(\%\) chance of winning when it doesn't snow, but only a 40\(\%\) chance of winning when it snows. Suppose there is a 50\(\%\) chance of snow. Make a tree diagram to find the probability that the team will win.

Graph the probability distribution described by each function. $$ P(x)=\frac{x}{10} \text { for } x=1,2,3, \text { and } 4 $$

A set of data has a normal distribution with a mean of 50 and a standard deviation of \(8 .\) Find the percent of data within each interval. less than 50

A data set has mean 25 and standard deviation \(5 .\) Find the \(z\) -score of each value. $$ 25 $$