Chapter 12

As a maintenance manager, Jackie Thomas is responsible for managing the maintenance of an office building. When entering a room after hours, the probability that she selects the correct key on the first try is \(\frac{1}{5} .\) If she enters 6 rooms in an evening, find each probability. \(P(\text { never the correct key })\)

The Millersburg school board is negotiating a pay raise with the teacher's union. Three of the administrators have salaries of \(\$ 90,000\) each. However, a majority of the teachers have salaries of about \(\$ 45,000\) per year. You are a member of the school board and would like to show that the current salaries are reasonable. Would you quote the mean, median, or mode as the “average” salary to justify your claim? Explain.

Janice has 8 DVD cases on a shelf, one for each season of her favorite TV show. Her brother accidentally knocks them off the shelf onto the floor. When her brother puts them back on the shelf, he does not pay attention to the season numbers and puts the cases back on the shelf randomly. Find each probability. P(all even-numbered seasons followed by all odd-numbered seasons)

Evaluate each expression. \(C(12,4) \cdot C(8,3)\)

For Exercises \(12-21,\) find the margin of sampling error to the nearest percent. Three hundred sixty-seven of 425 high school students said pizza was their favorite food in the school cafeteria.

As a maintenance manager, Jackie Thomas is responsible for managing the maintenance of an office building. When entering a room after hours, the probability that she selects the correct key on the first try is \(\frac{1}{5} .\) If she enters 6 rooms in an evening, find each probability. \(P(\text { always the correct key })\)

The Millersburg school board is negotiating a pay raise with the teacher's union. Three of the administrators have salaries of \(\$ 90,000\) each. However, a majority of the teachers have salaries of about \(\$ 45,000\) per year. You are the head of the teacher’s union and maintain that a pay raise is in order. Which of the mean, median, or mode would you quote to justify your claim? Explain your reasoning.

FOOD For Exercises \(20-23\) , use the following information. The shelf life of a particular snack chip is normally distributed with a mean of 180 days and a standard deviation of 30 days. About what percent of the products last between 150 and 210 days?

For Exercises \(20-23,\) determine whether the events are mutually exclusive or inclusive. Then find the probability. There are 4 algebra books, 3 literature books, and 2 biology books on a shelf. If a book is randomly selected, what is the probability of selecting a literature book or an algebra book?

Janice has 8 DVD cases on a shelf, one for each season of her favorite TV show. Her brother accidentally knocks them off the shelf onto the floor. When her brother puts them back on the shelf, he does not pay attention to the season numbers and puts the cases back on the shelf randomly. Find each probability. P(all even-numbered seasons in the correct position)

For Exercises \(12-21,\) find the margin of sampling error to the nearest percent. Nine hundred thirty-four of 2150 subscribers to a particular newspaper said their favorite sport was football.

JURY DUTY For Exercises \(21-23,\) use the following information. A jury of twelve people is being selected for trial. The probability that a juror will be male is \(0.5 .\) The probability that a juror will vote to convict is \(0.75 .\) What is the probability that more than 3 jurors will be men?

As a maintenance manager, Jackie Thomas is responsible for managing the maintenance of an office building. When entering a room after hours, the probability that she selects the correct key on the first try is \(\frac{1}{5} .\) If she enters 6 rooms in an evening, find each probability. \(P(\text { correct exactly } 4 \text { times })\)

The table lists the areas of some large shopping malls in the United States. Mall \(\qquad\) Gross Leasable Area \(\left(\mathrm{ft}^{2}\right)\) 1 Del Amo Fashion Center, Torrance, CA 3,000,000 2 South Coast Plaza/Crystal Court, Costa Mesa, CA 2,918,236 3 Mall of America, Bloomington, MN 2,472,500 4 Lakewood Center Mall, Lakewood, CA 2,390,000 5 Roosevelt Field Mall, Garden City, NY 2,300,000 6 Gurnee Mills, Gurnee, IL 2,200,000 7 The Galleria, Houston, TX 2,100,000 8 Randall Park Mall, North Randall, OH 2,097,416 9 Oakbrook Shopping Center, Oak Brook, IL 2,006,688 10 Sawgrass Mills, Sunrise, FL 2,000,000 10 The Woodlands Mall, The Woodlands, TX 2,000,000 10 Woodfi eld, Schaumburg, IL 2,000,000 Find the mean, median, and mode of the gross leasable areas.

FOOD For Exercises \(20-23\) , use the following information. The shelf life of a particular snack chip is normally distributed with a mean of 180 days and a standard deviation of 30 days. About what percent of the products last between 180 and 210 days?

For Exercises \(20-23,\) determine whether the events are mutually exclusive or inclusive. Then find the probability. A die is rolled. What is the probability of rolling a 5 or a number greater than 3\(?\)

The tiles \(E, T, F, U, N, X,\) and \(P\) of a word game are placed face down in the lid of the game. If two tiles are chosen at random, find each probability. \(P(X, \text { then } P),\) if no replacement occurs

Janice has 8 DVD cases on a shelf, one for each season of her favorite TV show. Her brother accidentally knocks them off the shelf onto the floor. When her brother puts them back on the shelf, he does not pay attention to the season numbers and puts the cases back on the shelf randomly. Find each probability. P(seasons 5 through 8 in any order followed by seasons 1 through 4 in any order)

Determine whether each situation involves a permutation or a combination. Then find the number of possibilities. the winner and first, second, and third runners-up in a contest with 10 finalists

The table lists the areas of some large shopping malls in the United States. Mall \(\qquad\) Gross Leasable Area \(\left(\mathrm{ft}^{2}\right)\) 1 Del Amo Fashion Center, Torrance, CA 3,000,000 2 South Coast Plaza/Crystal Court, Costa Mesa, CA 2,918,236 3 Mall of America, Bloomington, MN 2,472,500 4 Lakewood Center Mall, Lakewood, CA 2,390,000 5 Roosevelt Field Mall, Garden City, NY 2,300,000 6 Gurnee Mills, Gurnee, IL 2,200,000 7 The Galleria, Houston, TX 2,100,000 8 Randall Park Mall, North Randall, OH 2,097,416 9 Oakbrook Shopping Center, Oak Brook, IL 2,006,688 10 Sawgrass Mills, Sunrise, FL 2,000,000 10 The Woodlands Mall, The Woodlands, TX 2,000,000 10 Woodfi eld, Schaumburg, IL 2,000,000 You are a realtor who is trying to lease mall space in different areas of the country to a large retailer. Which measure would you talk about if the customer felt that the malls were too large for his store? Explain.

As a maintenance manager, Jackie Thomas is responsible for managing the maintenance of an office building. When entering a room after hours, the probability that she selects the correct key on the first try is \(\frac{1}{5} .\) If she enters 6 rooms in an evening, find each probability. \(P(\text { correct exactly } 2 \text { times })\)

FOOD For Exercises \(20-23\) , use the following information. The shelf life of a particular snack chip is normally distributed with a mean of 180 days and a standard deviation of 30 days. About what percent of the products last less than 90 days?

For Exercises \(20-23,\) determine whether the events are mutually exclusive or inclusive. Then find the probability. In the Math Club, 7 of the 20 girls are seniors, and 4 of the 14 boys are seniors. What is the probability of randomly selecting a boy or a senior to represent the Math Club at a statewide math contest?

The tiles \(E, T, F, U, N, X,\) and \(P\) of a word game are placed face down in the lid of the game. If two tiles are chosen at random, find each probability. \(P(2 \text { consonants), if no replacement occurs }\)

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(0 sophomores)

Determine whether each situation involves a permutation or a combination. Then find the number of possibilities. placing an algebra book, a geometry book, a chemistry book, an English book, and a health book on a shelf

As a maintenance manager, Jackie Thomas is responsible for managing the maintenance of an office building. When entering a room after hours, the probability that she selects the correct key on the first try is \(\frac{1}{5} .\) If she enters 6 rooms in an evening, find each probability. \(P(\text { no more than } 2 \text { times correct) }\)

FOOD For Exercises \(20-23\) , use the following information. The shelf life of a particular snack chip is normally distributed with a mean of 180 days and a standard deviation of 30 days. About what percent of the products last more than 210 days?

For Exercises \(20-23,\) determine whether the events are mutually exclusive or inclusive. Then find the probability. A card is drawn from a standard deck of cards. What is the probability of drawing an ace or a face card? (Hint: A face card is a jack, queen, or king.)

The tiles \(E, T, F, U, N, X,\) and \(P\) of a word game are placed face down in the lid of the game. If two tiles are chosen at random, find each probability. \(P(\text { selecting the same letter twice }),\) if no replacement occurs

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 sophomore)

How many ways can six different books be arranged on a shelf if one of the books is a dictionary and it must be on an end?

$$\begin{array}{|c|c|}\hline Score & {Frequency} \\ \hline 90 & {3} \\\ \hline 85 & {2} \\ \hline 80 & {3} \\ \hline 75 & {7} \\ \hline 70 & {6} \\\ \hline 65 & {4} \\ \hline\end{array}$$ Find the variance and standard deviation of the scores.

As a maintenance manager, Jackie Thomas is responsible for managing the maintenance of an office building. When entering a room after hours, the probability that she selects the correct key on the first try is \(\frac{1}{5} .\) If she enters 6 rooms in an evening, find each probability. \(P(\text { at least } 4 \text { times correct })\)

One tile with each letter of the alphabet is placed in a bag, and one is drawn at random. What is the probability of selecting a vowel or a letter from the word function?

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. \(P(\text { choosing } 2 \text { purple })\)

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(2 sophomores)

Determine whether each situation involves a permutation or a combination. Then find the number of possibilities. an arrangement of the letters in the word parallel

In how many orders can eight actors be listed in the opening credits of a movie if the leading actor must be listed first or last?

REASONING An exponential distribution function has a mean of 2. A fellow student says that the probability that \(x>2\) is \(0.5 .\) Determine whether this is sometimes, altways, or never true. Explain your reasoning.

Prisana guesses at all 10 true/false questions on her history test. Find each probability. \(P(\text { exactly } 6 \text { correct })\)

Each of the numbers from 1 to 30 is written on a card and placed in a bag. If one card is drawn at random, what is the probability that the number is a multiple of 2 or a multiple of 3\(?\)

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. \(P(\text { choosing } 2 \text { celebrity })\)

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(3 sophomores)

Determine whether each situation involves a permutation or a combination. Then find the number of possibilities. selecting two of eight employees to attend a business seminar

OPEN ENDED Give examples of a biased sample and an unbiased sample. Explain your reasoning.

Prisana guesses at all 10 true/false questions on her history test. Find each probability. \(P(\text { exactly } 4 \text { correct })\)

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

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. \(P(\text { choosing a yellow, then a purple) }\)

Determine whether each situation involves a permutation or a combination. Then find the number of possibilities. selecting nine books to check out of the library from a reading list of twelve