Chapter 12

Use the Internet or other resource to find the configuration of letters and numbers on license plates in your state. Then find the number of possible plates.

REASONING Explain what happens to the margin of sampling error when the size of the sample \(n\) increases. Why does this happen?

Jackson \(\qquad\) Washington \(\qquad\) King 170, 165, 140, 188, 195 \(\qquad\) 144, 177, 215, 225, 197 \(\qquad\) 166, 175, 196, 206, 219 Find the standard deviation of the weights for Jackson High.

Prisana guesses at all 10 true/false questions on her history test. Find each probability. \(P(\text { at most half correct })\)

OPEN ENDED Sketch a positively skewed graph. Describe a situation in which you would expect data to be distributed this way.

Two cards are drawn from a standard deck of cards. Find each probability. \(P(\text { both jacks or both face cards) }\)

Anita scores well enough at a carnival game that she gets to randomly draw two prizes out a prize bag. There are 6 purple T-shirts, 8 yellow T-shirts, and 5 T-shirts with a picture of a celebrity on them in the bag. Find each probability. \(P(\text { choosing a celebrity, then a yellow) }\)

Three students are selected at random from a group of 3 sophomores and 3 juniors. The table and relative-frequency histogram show the distribution of the number of sophomores chosen. Find each probability. \(\begin{array}{|c|c|c|c|}\hline 0 & {1} & {2} & {3} \\ \hline 1 & {\frac{9}{20}} & {\frac{9}{20}} & {\frac{1}{20}} \\ \hline\end{array}\) P(1 junior)

Determine whether each situation involves a permutation or a combination. Then find the number of possibilities. choosing two CDs to buy from ten that are on sale

Describe a situation in which you can use the Fundamental Counting Principle to show that there are 18 total possibilities.

Jackson \(\qquad\) Washington \(\qquad\) King 170, 165, 140, 188, 195 \(\qquad\) 144, 177, 215, 225, 197 \(\qquad\) 166, 175, 196, 206, 219 Find the standard deviation of the weights for Washington High.

Prisana guesses at all 10 true/false questions on her history test. Find each probability. \(P(\text { at least half correct })\)

CHALLENGE The graphing calculator screen shows the graph of a normal distribution for a large set of test scores whose mean is 500 and whose standard deviation is \(100 .\) If every test score in the data set were increased by 25 points, describe how the mean, standard deviation, and graph of the data would change.

Two cards are drawn from a standard deck of cards. Find each probability. \(P(\text { both face cards or both black) }\)

Tami, Sonia, Malik, and Roger are the four candidates for Student Council president. If their names are placed in random order on the ballot, what is the probability that Malik's name will be first on the ballot followed by Sonia's name second?

The state of Texas has a lottery in which 5 numbers out of 37 are drawn at random. What is the probability of a given ticket matching all 5 numbers?

Determine whether each situation involves a permutation or a combination. Then find the number of possibilities. selecting three of fifteen flavors of ice cream at the grocery store

REVIEW Your gym teacher is randomly distributing 15 red dodge balls and 10 yellow dodge balls. What is the probability that the first ball that she hands out will be yellow and the second will be red? $$ \begin{array}{ll}{\mathrm{F} \frac{1}{24}} & {\mathrm{H} \frac{2}{5}} \\\ {\mathrm{G} \frac{1}{4}} & {\mathrm{J} \frac{23}{25}}\end{array} $$

Jackson \(\qquad\) Washington \(\qquad\) King 170, 165, 140, 188, 195 \(\qquad\) 144, 177, 215, 225, 197 \(\qquad\) 166, 175, 196, 206, 219 Find the standard deviation of the weights for King High.

CARS According to a recent survey, about 1 in 3 new cars is leased rather than bought. What is the probability that 3 of 7 randomly selected new cars are leased?

Two cards are drawn from a standard deck of cards. Find each probability. \(P(\text { both either black or an ace) }\)

CHORES The five children of the Blanchard family get weekly chores assigned to them at random. Their parents put pieces of paper with the names of the five children in a hat and draw them out. The order of the names pulled determines the order in which the children will be responsible for sorting laundry for the next five weeks. What is the probability that Jim will be responsible for the first week and Emily will be responsible for the fifth week?

Use the table that shows the college majors of the students who took the Medical College Admission Test (MCAT) recently. $$\begin{array}{|l|l|}\hline \text { biological sciences } & {15,819} \\\ \hline \text { humanities } & {963} \\ \hline \text { math or statistics } & {179} \\ \hline \text { physical sciences } & {2770} \\ \hline \text { social sciences } & {2482} \\ \hline \text { specialized health sciences } & {1431} \\ \hline \text { other } & {1761} \\ \hline\end{array}$$ If a student taking the test were randomly selected, find each probability. Express as decimals rounded to the nearest thousandth. P(math or statistics)

Determine whether each situation involves a permutation or a combination. Then find the number of possibilities. How many ways can a hand of five cards consisting of four cards from one suit and one card from another suit be drawn from a standard deck of cards?

The members of the Math Club need to elect a president and a vice president. They determine that there are a total of 272 ways that they can fill the positions with two different members. How many people are in the Math Club?

REVIEW If \(x y^{-2}+y^{-1}=y^{-2},\) then the value of \(x\) cannot equal which of the following? $$ \begin{array}{l}{\mathbf{F}-1} \\ {\mathbf{G}\quad 0} \\ {\mathbf{H}\quad 1} \\\ {\mathbf{J} \quad 2}\end{array} $$

In a recent year, it was estimated that 55\(\%\) of U.S. adult Internet users had access to high-speed Internet connections at home or on the job. What is the probability that exactly 2 out of 5 randomly selected U.S. adults had access to high-speed Internet connections?

ACT/SAT If \(x+y=5\) and \(x y=6,\) what is the value of \(x^{2}+y^{2} ?\) $$ \begin{array}{l}{\text { A } 13} \\ {\text { B } 17} \\ {\text { C } 25} \\\ {\text { D } 37}\end{array} $$

GAMES For Exercises \(30-35\) , use the following information. A certain game has two stacks of 30 tiles with pictures on them. In the first stack of tiles, there are 10 dogs, 4 cats, 5 balls, and 11 horses. In the second stack of tiles, there are 3 flowers, 8 fish, 12 balls, 2 cats, and 5 horses. The top tile in each stack is chosen. Find each probability. \(P(\text { each is a ball })\)

Determine whether the events are independent or dependent. Then find the probability. There are 3 miniature chocolate bars and 5 peanut butter cups in a candy dish. Judie chooses 2 of them at random. What is the probability that she chose 2 miniature chocolate bars?

Use the table that shows the college majors of the students who took the Medical College Admission Test (MCAT) recently. $$\begin{array}{|l|l|}\hline \text { biological sciences } & {15,819} \\\ \hline \text { humanities } & {963} \\ \hline \text { math or statistics } & {179} \\ \hline \text { physical sciences } & {2770} \\ \hline \text { social sciences } & {2482} \\ \hline \text { specialized health sciences } & {1431} \\ \hline \text { other } & {1761} \\ \hline\end{array}$$ If a student taking the test were randomly selected, find each probability. Express as decimals rounded to the nearest thousandth. P(biological sciences)

Determine whether each situation involves a permutation or a combination. Then find the number of possibilities. A student council committee must be composed of two juniors and two sophomores. How many different committees can be chosen from seven juniors and five sophomores?

A student guesses at all 5 questions on a true-false quiz. Find each probability. \(P(\text { all } 5 \text { correct })\)

A set of 260 data values is normally distributed with a mean of 50 and a standard deviation of \(5.5 .(\text { (lesson } 12-7)\) What is the probability that a data value selected at random is greater than 39\(?\)

If a thumbtack is dropped, the probability of it landing point-up is \(0.3 .\) If 10 tacks are dropped, find each probability. \(P(\text { at least } 8 \text { points up })\)

REVIEW Jessica wants to create several different 7 -character passwords. She wants to use arrangements of the first three letters of her name, followed by arrangements of 4 digits in 1987 , the year of her birth. How many different passwords can she create? $$ \begin{array}{llllllll}{F} & {672} & {G} & {288} & {H} & {576} & {} & {J} & {144}\end{array} $$

GAMES For Exercises \(30-35\) , use the following information. A certain game has two stacks of 30 tiles with pictures on them. In the first stack of tiles, there are 10 dogs, 4 cats, 5 balls, and 11 horses. In the second stack of tiles, there are 3 flowers, 8 fish, 12 balls, 2 cats, and 5 horses. The top tile in each stack is chosen. Find each probability. \(P(\text { neither is a horse) }\)

Determine whether the events are independent or dependent. Then find the probability. A cage contains 3 white and 6 brown hamsters. Maggie randomly selects one, puts it back, and then randomly selects another. What is the probability that both selections were white?

Use the table that shows the college majors of the students who took the Medical College Admission Test (MCAT) recently. $$\begin{array}{|l|l|}\hline \text { biological sciences } & {15,819} \\\ \hline \text { humanities } & {963} \\ \hline \text { math or statistics } & {179} \\ \hline \text { physical sciences } & {2770} \\ \hline \text { social sciences } & {2482} \\ \hline \text { specialized health sciences } & {1431} \\ \hline \text { other } & {1761} \\ \hline\end{array}$$ If a student taking the test were randomly selected, find each probability. Express as decimals rounded to the nearest thousandth. P(physical sciences)

Determine whether each situation involves a permutation or a combination. Then find the number of possibilities. How many ways can a hand of five cards consisting of three cards from one suit and two cards from another suit be drawn from a standard deck of cards?

How many numbers between 100 and 999, inclusive, have 7 in the tens place? A. 90 B. 100 C. 110 D. 120

A student guesses at all 5 questions on a true-false quiz. Find each probability. \(P(\text { exactly } 4 \text { correct })\)

A die is rolled, Find each probability. \(P(\text { even })\)

If a thumbtack is dropped, the probability of it landing point-up is \(0.3 .\) If 10 tacks are dropped, find each probability. \(P(\text { at most } 3 \text { points up })\)

Find the variance and standard deviation of each set of data to the nearest tenth. $$ \\{7,16,9,4,12,3,9,4\\} $$

Determine whether the events are independent or dependent. Then find the probability. A bag contains 7 red, 4 blue, and 6 yellow marbles. If 3 marbles are selected in succession, what is the probability of selecting blue, then yellow, then red, if replacement occurs each time?

The game of euchre (YOO ker) is played using only the 9s, 10s, jacks, queens, kings, and aces from a standard deck of cards. Find the probability of being dealt a 5-card hand containing all four suits.

The manager of a four-screen movie theater is deciding which of 12 available movies to show. The screens are in rooms with different seating capacities. How many ways can she show four different movies on the screens?

A coin is tossed four times. How many possible sequences of heads or tails are possible? F. 4 G. 8 H. 16 J. 32

A student guesses at all 5 questions on a true-false quiz. Find each probability. \(P(\text { at least } 3 \text { correct })\)