Gallery Problems Exercise

Gallery Problems Exercise

Chance of Rain

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Chance of Rain

On Friday morning, Joey hears this weather report: There is an 80% chance of rain on Saturday and an 80% chance of rain on Sunday.

Joey says, “That means there is an 80% chance that it will rain on at least one day this weekend.” Joey is wrong.

  1. What is the chance that it will rain on at least one day during the weekend? Justify your answer mathematically.

Penguins

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Penguins

In an Antarctic penguin colony, 200 penguins are captured, tagged, and released. A year later, 100 penguins are captured, and 4 of them have the tags from the year before.

  1. Based on this sample, how many penguins are in the colony?
  2. Does this sample provide enough evidence to make a reasonable estimate about how many penguins are in the colony?

How Many Yellow?

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How Many Yellow?

There are 60 balls in a bag. Each ball is red, green, or yellow.

The probability of drawing a red ball is 25.

The probability of drawing a green ball is 13.

  1. How many yellow balls are there in the bag? Justify your answer mathematically.

How Many Ways to Line Up?

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How Many Ways to Line Up?

Five students, Al, Bob, Carlos, Danica, and Ella, are early for math class and stand in line. They begin to talk about how many ways they could line up.

Find the number of ways that they can line up. Consider the following:

  1. How many ways are there if Al is first in line?
  2. How many ways are there if Al is first and Bob is second?
  3. Think of a systematic way to find all of the possibilities.

Gumballs

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Gumballs

There are 3 red and 6 white gumballs left in a machine.

  1. If Sarah buys 2 gumballs, what are the chances that at least 1 gumball will be red? Show your work and justify your thinking.

New Family

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New Family

A newly married couple wants to have 4 children.

  1. What is the probability that they will have 2 boys and 2 girls? Show your work and justify your thinking.

Nickel and Dime

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Nickel and Dime

Marisa flips a dime and a nickel at the same time. Both coins are fair―that is, the probability of getting heads is 1212.

  1. What is the probability that the nickel is heads? Explain why.
  2. What is the probability that both coins are heads? Explain why.
  3. What is the probability that only one coin is heads? Explain why.

Four More Flips

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Four More Flips

Alex decides to flip a coin 6 times. He will record the results.

His first 2 flips are tails.

  1. After Alex flips the coin 4 more times, what is the most likely number of tails in his set of 6 flips? Justify your answer mathematically.

Bubble Gum

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Bubble Gum

A gum company has a contest. The winner is the first to collect the letters G, U, and M printed inside the bubble gum wrappers. One of the letters G, U, or M is printed inside each bubble gum wrapper in a ratio of 3:2:1. How many packages of bubble gum would you need to open to get each letter?

  1. Use a simulation to model the probability that you will win if you buy 10 packages of gum.
  2. How many packages would you need to buy to have a 50% chance of winning?

A Large Family

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A Large Family

A newly married couple would like to have 3 girls. How many children are they likely to have in order to have 3 girls?

  1. Use a simulation  to model the probability that they will have 3 girls by the time they have 6 children.

No Telephone

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No Telephone

For each one of the 50 states, the U.S. Census Bureau reports the percent of households without a telephone. Some states have a higher percent of households without a telephone. Other states have lower percentages.

The box plots summarize these state-by-state data for two different years—1960 and 1990.

  1. What do the box plots tell you about how telephone ownership in the 50 states changed from 1960 to 1990? Give as much specific information as you can.

Pulse Rate

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Pulse Rate

The resting pulse rate (beats per minute) is shown for a group of athletes and for a group of students. Compare the two sets of data, taking into account that they are of different sizes.

Athletes: 48, 50, 52, 53, 56, 60, 63, 64, 66, 70, 71, 72

Students: 63, 66, 66, 74, 78, 79, 80, 90

  1. Which group has an overall lower heart rate?

Golf Scores

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Golf Scores

Rosa and Chen love to play golf. Rosa’s scores for seven rounds were 105, 79, 98, 84, 75, 99, and 110. Chen’s scores were 88, 86, 90, 86, 75, 110, and 87.

Make two box plots to show the data. Be sure to use the same scale and align the same values with each other.

Compare and contrast the box plots.

  1. Which features of the two data sets are the same?
  2. Look at the interquartile range for both data sets. Use this statistic to comment on the golfing skills of Rosa and Chen.
  3. Compare the upper whiskers of both graphs. What does this information tell you?
  4. Which of the box plots is more symmetrical? What does this information tell you about the data distribution in the box plot?
  5. How do the medians, ranges, and interquartile ranges compare, and which of these statistics tell you who the better golfer is? Explain your answer.

How Much Taller?

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How Much Taller?

Basketball: 60, 67, 68, 68, 69, 70, 72, 73, 73, 74

Soccer: 57, 58, 59, 60, 60, 62, 65, 66, 66, 72

  1. Given the heights of the seventh-grade basketball team and the seventh-grade soccer team, in inches, decide which group is taller using the statistics tools of your choice.
  2. Calculate the MAD for both groups.

Coin Jar

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Coin Jar

Given the sample, estimate how much money is in the jar.

Each coin weighs a specific amount:

Penny: 2.500 g

Nickel: 5.000 g

Dime: 2.268 g

Quarter: 5.670 g

  1. Think about the weight of each coin in the sample and what the ratio would be to the total weight of the sample and the coins in the jar.

Project Work Time

Project Work Time

You can choose to work on and complete your project and/or get help if needed.