AQR Unit 4

72

1. A yogurt shop offers 6 different flavors of frozen yogurt and 12 different toppings. How many choices are possible for a single serving of frozen yogurt with one topping?

40,320

2. In how many different orders can you line up 8 cards on a table?

90 ways

3. There are 10 students participating in a spelling bee. In how many ways can the students who go first and second in the bee be chosen?

6,844/91

4. Evaluate 60C3/15C3

57

5. There are 6 people on the ballot for regional judges. Voters can vote for any 4. Voters can choose to vote for 0, 1, 2, 3, or 4 judges. In how many different ways can a person vote?

5/8

1. A bag contains 6 red marbles, 6 white marbles, and 4 blue marbles. Find P (red or blue).

Using the digits 0-6 to represent a caught fish, the probability of catching a fish on each of the
next three days is 35%.

2. A biologist has determined that a particular osprey has a 70% chance of catching a fish on any given day. Carry out a simulation of 20 trials using the random number table below to find the probability that the osprey will actually catch a fish on all of the next three days. Explain your method. 945 025 354 793 236 106 746 981 105 012 832 180 250 871 835 793 726 864 496 947

3/8

3. This is a spinner used in a board game. What is the probability that the spinner will land on a multiple of 3 and 4?

94/54145

4. What is the theoretical probability of being dealt exactly three 4s in a 5-card hand from a standard 52- card deck?

1/16

5. If a dart hits the target at random, what is the probability that it will land in the shaded region?

Taking two marbles from a box without replacing the first marble

1. Which are dependent events?

0.1804

2. Suppose Q and R are independent events. Find P(Q and R). P(Q) = 0.41, P(R) = 0.44

Rolling an even number and an odd number

3. You roll a six-sided number cube. Which events are mutually exclusive?

42%

4. Suppose S and T are mutually exclusive events. Find P(S or T). P(S) = 20%, P(T) = 22%

9/11

5. A jar contains 7 blue cubes, 4 blue spheres, 5 green cubes, and 6 green spheres. If you select an object at random, what is the probability that the object is green or a cube?

15

1. Suppose Ruth Ann has 3 routes she can travel between the school to the library, and 5 routes from the library to her home. How many routes are there from Ruth Ann’s school to her home with a stop at the library?

696

2. Verne has 6 math books to line up on a shelf. Jenny has 4 English books to line up on a shelf. In how many more orders can Verne line up his books than Jenny?

7

3. Evaluate 7C6

10

4. In how many ways can 3 singers be selected from 5 who came to an audition?

0

5. A bag contains 8 red marbles, 4 white marbles, and 5 blue marbles. You draw one marble at random. Find P(red and blue).

2/5

6. A spinner is numbered from 1 through 10 with each number equally likely to occur. What is the probability of obtaining a number less than 2 or greater than 7 in a single spin?

3/16

7. On the following dartboard, the radius of the bullseye (area A) is 4 inches. The radius of each concentric circle is 4 inches more than the circle inside it. If a person throws randomly onto the dartboard, what is the probability that the dart will hit in area B?

4/11

8. Two urns contain white balls and yellow balls. The first urn contains 9 white balls and 9 yellow balls and the second urn contains 8 white balls and 3 yellow balls. A ball is drawn at random from each urn. What is the probability that both balls are white?

0.9

9. If all possible results are equally likely, what is the probability that a spin of the spinner will land on an upper case letter or a consonant?

16/21

10. Joey’s sock drawer is unorganized and contains 3 black dress socks, 5 black ankle socks, 7 brown dress socks, and 6 brown ankle socks. What is the probability that Joey will blindly reach into his sock drawer and pull out a sock that is brown or a dress sock?

0.565

11. The table shows the results of a survey of students in two math classes. Find P(more than 1 hour of TV | 6th period class). Round to the nearest thousandth. Did You Watch More Than One Hour of TV Last Night?

79.8%

12. The probability that a city bus is ready for service when needed is 84%. The probability that a city bus is ready for service and has a working radio is 67%. Find the probability that a bus chosen at random has a working radio given that it is ready for service. Round to the nearest tenth of a percent.

0.241

13. A class of 40 students has 11 honor students and 10 athletes. Three of the honor students are also athletes. One student is chosen at random. Find the probability that this student is an athlete if it is known that the student is not an honor student. Round to the nearest thousandth.

Mean = 9.3
Median = 10
Mode = 13

1. Find the mean, median, and mode of the data set. Round to the nearest tenth. 15, 13, 9, 9, 7, 1, 11, 10, 13, 1, 13

38

2. Find the outlier in the set of data. 17, 13, 16, 18, 38, 14, 21, 24

Mean = 13,156
Median = 12,700
No mode
The median is the best choice because it is not skewed by the high outlier

3. Over the first five years of owning a car, Gina drove about 12,700 miles the first year, 15,478 miles the second year, 12,675 the third year, 11,850 the fourth year, and 13,075 the fifth year. a. Find the mean, median, and mode of this data. b. Explain which measure of central tendency will best predict how many miles Gina will drive in the sixth year.

A

4. Make a box-and-whisker plot of the data. 24, 18, 29, 21, 16, 23, 13, 11

30th percentile = 7
90th percentile = 19

5. Find the values of the 30th and 90th percentiles of the data. 18, 9, 7, 5, 11, 7, 17, 20, 19, 2, 17, 12, 5, 1, 13, 12, 11, 15, 16, 20

Mean = 87.5
Variance = 245.6
Standard deviation = 15.7

1. What are the mean, variance, and standard deviation of these values? Round to the nearest tenth. 92, 97, 53, 90, 95, 98

Mean = 47.6
Variance = 31
Standard deviation = 5.6

2. What are the mean, variance, and standard deviation of these values? Round to the nearest tenth.

2

3. Susan keeps track of the number of tickets sold for each play presented at the community theater. Within how many standard deviations of the mean do all the values fall? 135, 71, 69, 80, 158, 152, 161, 96, 122, 118, 87, 85

2

4. The graph below displays how many pieces of candy Timmy and his five friends each received last Halloween. Within how many standard deviations of the mean do the values fall?

Convenience sample

1. A citizens’ group wants to determine peoples’ opinions about a new road. The members of the group conduct a survey at the largest mall in the city. Which best describes the sampling method used by the citizens’ group?

Do you think we should plant gardens in the park or buy new park benches?

2. The town council must decide how to allocate next year’s budget. They survey a sample of the town population to determine residents’ preferences. Which survey question shows the least bias?

Go to every fifth house and ask the working adults, "How many times per week do you ride the
bus to work?"

3. You want to determine what percentage of working adults in your neighborhood regularly ride the bus to work. Which sampling method and survey question are best?

50

4. A researcher tags 20 squirrels in a wood. The next month, she returns to the wood and observes a sample of 12 squirrels, 5 of which are tagged, and a sample of 25 squirrels, 9 of which are tagged. If the two samples are representative of the squirrel population, which is the best estimate of the number of squirrels in the wood?

91%

1. A survey of high school juniors found that 82% of students plan on attending college. If you pick three students at random, what is the probability that at least two plan on attending college? Round to the nearest percent.

5.1%

2. A poll shows that 76% of voters in a city favor an initiative to increase spending on public schools. If 10 voters are selected at random, what is the probability that exactly five of them will vote in favor of the initiative?

C

3. Use the Binomial Theorem to find the binomial expansion of the expression. (s – 5v)^5

55.8%

4. A recent poll found that 45% of eligible voters are planning to vote in favor of a new by-law. Suppose you randomly survey six voters. What is the probability that at least three of the voters plan to vote in favor of the new by-law?

Mean = 75.8
Median = 76.5
Mode = 63

1. Find the mean, median, and mode of the data set. Round to the nearest tenth. Test scores on a math exam: 88, 89, 65, 62, 83, 63, 84, 63, 74, 64, 71, 82, 66, 88, 79, 60, 86, 63, 93, 99, 60, 85

A

2. Make a boxandwhisker plot of the data. Average daily temperatures in Tucson, Arizona, in December: 67, 57, 52, 51, 64, 58, 67, 58, 55, 59, 66, 50, 57, 62, 58, 50, 58, 50, 60, 63

30th percentile = 105
90th percentile = 176

3. Find the values of the 30th and 90th percentiles of the data. 129, 113, 200, 100, 105, 132, 100, 176, 146, 152

Mean = 8
Variance = 18.3
Standard deviation = 4.3

4. What are the mean, variance, and standard deviation of these values? Round to the nearest tenth. 11, 11, 3, 1, 11, 11

2

5. Mrs. Jones Algebra 2 class scored very well on yesterday’s quiz. With one exception, everyone received an A. Within how many standard deviations of the mean do all the quiz grades fall? 91, 92, 94, 88, 96, 99, 91, 93, 94, 97, 95, 97

22%

6. According to one study, 61% of the population swallow at least one spider per year in their sleep. Based on this study, what is the probability that exactly 7 of 10 randomly selected people have swallowed at least one spider in their sleep in the last year.

D

7. Use the Binomial Theorem to find the binomial expansion of the expression. (d-5)^6

93%

8. The bar graph shows the rents paid per month for apartments in an urban neighborhood. The curve shows that the rents are normally distributed. Estimate the percent of apartment residents who pay from $600 to $749 per month.

16%

9. The scores on an exam are normally distributed with a mean of 77 and a standard deviation of 10. What percent of the scores are greater than 87?

84%

10. A grocery store will only accept yellow onions that are at least 3 in. in diameter. A grower has a crop of onions with diameters that are normally distributed with a mean diameter of 3.25 in. and a standard deviation of 0.25 in. What percent of the onions will be accepted by the grocery store?

479,001,600

1. In how many ways can 12 basketball players be listed in a program?

3,024

2. Evaluate 9P4

30

3. The Booster Club sells meals at basketball games. Each meal comes with a choice of hamburgers, pizza, hot dogs, cheeseburgers, or tacos, and a choice of root beer, lemonade, milk, coffee, tea, or cola. How many possible meal combinations are there?

11/20

4. Lynn and Dawn tossed a coin 60 times and got heads 33 times. What is the experimental probability of tossing heads using Lynn and Dawn’s results?

27/29

5. Teesha is in the French club. There are 29 students in the club. The French teacher will pick two students at random to guide visiting students from France. What is the probability that Teesha will not be picked as a guide?

20%

6. A game uses 26 tiles, lettered from A to Z. To start, you randomly choose a set of 5 tiles. What is the theoretical probability of drawing exactly 2 vowels (A, E, I, O, or U) in your set of 5? Round to the nearest percent.

4 inches

7. A dartboard consists of two concentric circles. The probability of hitting the inner circle is 16%. If the outer circle has a diameter of 20 inches, what is the radius of the inner circle?

46.7%

8. Eli has 7 black pens and 5 blue pens in his desk drawer. He also has 3 yellow highlighters, 2 green highlighters, and 5 pink highlighters in his pencil case. If he chooses one pen and one highlighter without looking, what is the probability that he will get a black pen and he will not get a green highlighter?

0.813

9. Using a sixteen-sided number cube, what is the probability that you will roll an even number or an odd prime number? The number 1 isn’t an odd prime. Round to three decimals.

0.464

10. Each person in a group of students was identified by year and asked when he or she preferred taking classes: in the morning, afternoon, or evening. The results are shown in the table. Find the probability that the student preferred afternoon classes given he or she is a junior. Round to the nearest thousandth.

34.2%

11. The probability that a dessert sold at a certain cafe contains chocolate is 73%. The probability that a dessert containing chocolate also contains nuts is 25%. Find the probability that a dessert chosen at random contains nuts given that it contains chocolate. Round to the nearest tenth of a percent.

0.85

12. An airline has 81% of its flights depart on schedule. It has 69% of its flights depart and arrive on schedule. Find the probability that a flight that departs on schedule also arrives on schedule.

30th percentile = 7
90th percentile = 19

13. Find the values of the 30th and 90th percentiles of the data. 18, 9, 7, 5, 11, 7, 17, 20, 19, 2, 17, 12, 5, 1, 13, 12, 11, 15, 16, 20

A

14. Use the Binomial Theorem to find the binomial expansion of the expression. (d + 3)7

30%

15. The bar graph shows the rents paid per month for apartments in an urban neighborhood. The curve shows that the rents are normally distributed. Estimate the percent of apartment residents who pay less than $650 per month.

25 bags

16. Betty’s Bite-Size Candies are packaged in bags. The number of candies per bag is normally distributed, with a mean of 50 candies and a standard deviation of 3. At a quality control checkpoint, a sample of bags is checked, and 4 bags contain fewer than 47 candies. How many bags were probably taken as samples?