Resources

Resources

Find probabilities using the binomial distribution

p(t)=100\left(\dfrac{1}{2}\right)^{\dfrac{t}{8.02}}

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Radioactive isotopes are unstable atoms that decay into other atoms. Iodine

-131

is a radioactive isotope. The function models

p

, the percentage of iodine

-131

atoms remaining in a sample after

t

days. To the nearest tenth of a percent, what percent of iodine

-131

atoms remain in the sample after

10

Jose is going to use a random number generator

500

times. Each time he uses it, he will get a

1,2,3

4

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Complete the following statement with the best prediction.

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Jose will get something other than a

2 \ldots

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1

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250

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250

times but probably not exactly

250

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375

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375

times but probably not exactly

375

Leo is going to use a random number generator

400

times. Each time he uses it, he will get a

1,2,3,4

5

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What is the best prediction for the number of times that Leo will get an odd number?

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1

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133

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133

times but probably not exactly

133

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240

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240

times but probably not exactly

240

According to an autograph association, only

5 \%

of autographs in circulation from a certain band are estimated to be real. If there are

77

authentic autographs of the band in circulation, then how many nonauthentic autographs are there in circulation?

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\square

nonauthentic autographs in circulation.

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(Round to the nearest integer as needed.)

An underwater (but near the surface) explosion is detected by sonar on a ship

30 \mathrm{~s}

before it is heard on the deck. If sound travels at

800 \mathrm{~m} / \mathrm{s}

310 \mathrm{~m} / \mathrm{s}

in air, how far is the ship from the explosion (to

3

significant digits)?

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The distance from the ship to the location of the explosion is

\_\_\_\_\_\mathrm{~m}

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(Do not round until the final answer. Then round to the nearest hundred as needed.)

Laney went to the park and collected some cool rocks. She had four shiny *

4

puntos rocks, three blue rocks, and two rocks with holes. On the way to her vehicle, she lost two blue rocks. What is the probability of her friend picking a shiny rock out of her bag?

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4 / 9

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4 / 8

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4 / 7

Kadeem has a bag that contains pineapple chews, apple chews, and watermelon chews. He performs an experiment. Kadeem randomly removes a chew from the bag, records the result, and returns the chew to the bag. Kadeem performs the experiment

21

times. The results are shown below:

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A pineapple chew was selected

6

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A apple chew was selected

10

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A watermelon chew was selected

5

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If the experiment is repeated

900

more times, about how many times would you expect Kadeem to remove a apple chew from the bag? Round your answer to the nearest whole number.

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The actual dimensions of a rectangle are

10 \mathrm{~cm}

9 \mathrm{~cm}

. Carter measures the sides to be

9.9 \mathrm{~cm}

8.97 \mathrm{~cm}

. In calculating the area, what is the relative error, to the nearest thousandth.

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The volume of a rectangular prism is

168 \mathrm{ft}^{3}

. David measures the sides to be

6.84 \mathrm{ft}

2.82 \mathrm{ft}

8.11 \mathrm{ft}

. In calculating the volume, what is the relative error, to the nearest thousandth.

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The volume of a rectangular prism is

18 \mathrm{~cm}^{3}

. David measures the sides to be

2.88 \mathrm{~cm}

1.53 \mathrm{~cm}

3.49 \mathrm{~cm}

. In calculating the volume, what is the relative error, to the nearest thousandth.

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The volume of a rectangular prism is

84 \mathrm{ft}^{3}

. David measures the sides to be

3.91 \mathrm{ft}

2.84 \mathrm{ft}

7.35 \mathrm{ft}

. In calculating the volume, what is the relative error, to the nearest thousandth.

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Fawzia owns a small business selling used books. She knows that in the last week

45

customers paid cash,

10

customers used a debit card, and

64

customers used a credit card.

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Based on these results, express the probability that the next customer will pay with a debit card as a decimal to the nearest hundredth.

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Amadou has a bag that contains orange chews, cherry chews, and watermelon chews. He performs an experiment. Amadou randomly removes a chew from the bag, records the result, and returns the chew to the bag. Amadou performs the experiment

36

times. The results are shown below:

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An orange chew was selected

10

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A cherry chew was selected

20

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A watermelon chew was selected

6

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Based on these results, express the probability that the next chew Amadou removes from the bag will be cherry chew as a decimal to the nearest hundredth.

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Through ten games of basketball this season, Ava has made

10

12

of her freethrows. Which word or phrase describes the probability that Ava will hit her next free throw?

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an equal chance or

50-50

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Bentley buys a ticket for a raffle with several prizes. The probability that he wins a prize is

89 \%

. Which word or phrase describes the probability that Bentley will win a prize?

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an equal chance or

50-50

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Chase has a bag that contains pineapple chews, cherry chews, and watermelon chews. He performs an experiment. Chase randomly removes a chew from the bag, records the result, and returns the chew to the bag. Chase performs the experiment

56

times. The results are shown below:

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A pineapple chew was selected

22

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A cherry chew was selected

22

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A watermelon chew was selected

12

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Based on these results, express the probability that the next chew Chase removes from the bag will be a flavor other than pineapple as a decimal to the nearest hundredth.

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Faith owns a small business selling clothing. She knows that in the last week

86

customers paid cash,

15

customers used a debit card, and

40

customers used a credit card.

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Based on these results, express the probability that the next customer will pay with something other than a debit card as a decimal to the nearest hundredth.

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Josiah has a bag that contains strawberry chews, apple chews, and watermelon chews. He performs an experiment. Josiah randomly removes a chew from the bag, records the result, and returns the chew to the bag. Josiah performs the experiment

30

times. The results are shown below:

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A strawberry chew was selected

9

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A apple chew was selected

15

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A watermelon chew was selected

6

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Based on these results, express the probability that the next chew Josiah removes from the bag will be a flavor other than strawberry as a percent to the nearest whole number.

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Zendaya has a bag that contains orange chews, cherry chews, and watermelon chews. She performs an experiment. Zendaya randomly removes a chew from the bag, records the result, and returns the chew to the bag. Zendaya performs the experiment

24

times. The results are shown below:

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A orange chew was selected

13

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A cherry chew was selected

5

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A watermelon chew was selected

6

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Based on these results, express the probability that the next chew Zendaya removes from the bag will be cherry or watermelon as a decimal to the nearest hundredth.

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Easton owns a small business selling clothing. He knows that in the last week

40

customers paid cash,

25

customers used a debit card, and

46

customers used a credit card.

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Based on these results, express the probability that the next customer will pay with something other than a credit card as a decimal to the nearest hundredth.

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Jamal has a bag that contains orange chews, apple chews, and peach chews. He performs an experiment. Jamal randomly removes a chew from the bag, records the result, and returns the chew to the bag. Jamal performs the experiment

33

times. The results are shown below:

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A orange chew was selected

15

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A apple chew was selected

4

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A peach chew was selected

14

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Based on these results, express the probability that the next chew Jamal removes from the bag will be a flavor other than peach as a decimal to the nearest hundredth.

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Kayden has a bag that contains pineapple chews, lemon chews, and lime chews. He performs an experiment. Kayden randomly removes a chew from the bag, records the result, and returns the chew to the bag. Kayden performs the experiment

45

times. The results are shown below:

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A pineapple chew was selected

34

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A lemon chew was selected

7

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A lime chew was selected

4

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Based on these results, express the probability that the next chew Kayden removes from the bag will be lemon chew as a fraction in simplest form.

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Violet has a bag that contains strawberry chews, apple chews, and peach chews. She performs an experiment. Violet randomly removes a chew from the bag, records the result, and returns the chew to the bag. Violet performs the experiment

44

times. The results are shown below:

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A strawberry chew was selected

3

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A apple chew was selected

17

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A peach chew was selected

24

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Based on these results, express the probability that the next chew Violet removes from the bag will be strawberry or peach as a decimal to the nearest hundredth.

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Through ten games of basketball this season, Nathaniel has made

3

15

of his free-throws. Which word or phrase describes the probability that Nathaniel will hit his next free throw?

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an equal chance or

50-50

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Through ten games of basketball this season, Amelia has made

5 \%

of her free-throws. Which word or phrase describes the probability that Amelia will hit her next free throw?

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an equal chance or

50

-50

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Cai's school is selling

100

raffle-tickets to raise money for a new gymnasium. The grand-prize is a ten-speed mountain bike. Which word or phrase describes the probability that he will win the raffle if he buys all the tickets?

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an equal chance or

50-50

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A spinner for a board-game is divided into four equal-sized sections colored red, green, yellow, and blue. If you land on a line between the colors, you keep spinning until you land on a color. Mamadou's turn is next. Which word or phrase describes the probability that he will land on yellow or blue or green?

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Marques' school is selling

100

raffle-tickets to raise money for a new gymnasium. The grand-prize is a ten-speed mountain bike. Which word or phrase describes the probability that he will win the raffle if he buys all the tickets?

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an equal chance or

50-50

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E. coli is among the fastest-growing bacteria, with a generation (or doubling) time of

20

minutes under optimal conditions. After

60

minutes, the number of bacteria in a culture of E. coli was

400

. Approximately how many bacteria were in the culture after

30

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1

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50

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142

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174

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200

inference about the data is best supported by this information?

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More eighth-grade students prefer art as an elective than prefer band

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Fewer seventh-grade students prefer band or theater as an elective tha art.

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Half as many seventh-grade students as eighth-grade students prefer t an elective.

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Twice as many seventh-grade students as eighth-grade student prefer

According to the latest financial reports from a sporting goods store, the mean sales per customer was

\$75

with a population standard deviation of

\$6

. The store manager believes

39

randomly selected customers spent more per transaction.

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Use a calculator to find the probability that the sample mean of sales per customer is between

\$76

\$77

dollars. Round to two decimal places.

How much money should be deposited today in an account that earns

3\%

compounded semiannually so that it will accumulate to

\$12,000

in three years?

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The amount of money that should be deposited is

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\$\square

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(Round up to the nearest cent.)

A large company put out an advertisement in a magazine for a job opening. The first day the magazine was published the company got

160

responses, but the responses were declining by

15 \%

each day. Assuming the pattern continued, how many total responses would the company get over the course of the first

21

days after the magazine was published, to the nearest whole number?

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A large company put out an advertisement in a magazine for a job opening. The first day the magazine was published the company got

160

responses, but the responses were declining by

15 \%

each day. Assuming the pattern continued, how many total responses would the company get over the course of the first

5

days after the magazine was published, to the nearest whole number?

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A large company put out an advertisement in a magazine for a job opening. The first day the magazine was published the company got

120

responses, but the responses were declining by

10 \%

each day. Assuming the pattern continued, how many total responses would the company get over the course of the first

9

days after the magazine was published, to the nearest whole number?

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A large company put out an advertisement in a magazine for a job opening. The first day the magazine was published the company got

184

responses, but the responses were declining by

25 \%

each day. Assuming the pattern continued, how many total responses would the company get over the course of the first

9

days after the magazine was published, to the nearest whole number?

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26

7

play an instrument and

9

play a sport. There are

5

students who play an instrument and also play a sport. What is the probability that a student who plays an instrument also plays a sport?

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21

5

have a brother and

8

have a sister. There are

10

students who do not have any siblings. What is the probability that a student who has a sister also has a brother?

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27

10

have a brother and

9

have a sister. There are

15

students who do not have any siblings. What is the probability that a student who has a brother also has a sister?

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Last year at a certain high school, there were

100

ninth graders on the honor roll and

95

tenth graders on the honor roll. This year, the number of ninth graders on the honor roll increased by

5 \%

and the number of tenth graders on the honor roll increased by

20 \%

. By what percentage did the total number of students on the honor roll increase? Round your answer to the nearest tenth (if necessary).

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Last year at a certain high school, there were

92

ninth graders on the honor roll and

110

tenth graders on the honor roll. This year, the number of ninth graders on the honor roll increased by

25 \%

and the number of tenth graders on the honor roll increased by

20 \%

. By what percentage did the total number of students on the honor roll increase? Round your answer to the nearest tenth (if necessary).

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Last year at a certain high school, there were

52

ninth graders on the honor roll and

150

tenth graders on the honor roll. This year, the number of ninth graders on the honor roll decreased by

25 \%

and the number of tenth graders on the honor roll decreased by

2 \%

. By what percentage did the total number of students on the honor roll decrease? Round your answer to the nearest tenth (if necessary).

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5

.) An actuary discovers that policyholders are three times as likely to file

2

claims as to file

4

claims. If the number of claims filed follows a Poisson distribution, what is the standard deviation of the number of claims filed?

For the following set of data, find the population standard deviation, to the nearest thousandth.

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118,83,54,162,83,42,133

At a local restaurant, the amount of time that customers have to wait for their food is normally distributed with a mean of

28

minutes and a standard deviation of

3

minutes. If you visit that restaurant

44

times this year, what is the expected number of times that you would expect to wait longer than

34

minutes, to the nearest whole number?

In an all boys school, the heights of the student body are normally distributed with a mean of

71

inches and a standard deviation of

4

5

inches. Out of the

993

boys who go to that school, how many would be expected to be between

63

72

inches tall, to the nearest whole number?

Since the stock market began in

1872

, stock prices have risen in about

73\%

of the years. Assuming that market performance is independent from year to year, what's the probability that the market will fall during at least

1

5