Cameron's scout leader organized a contest to see who could build the strongest boat out of aluminum foil. After building their boats, the scouts measured how many pennies the boats could support before sinking. This box plot shows the results.

Pennies supported
0
4
8
12
16
20
What fraction of the boats could support 12 or more pennies?

1 answer

To determine the fraction of boats that could support 12 or more pennies based on the box plot results, we will analyze the provided information:

  1. Identify the total number of boats: The box plot typically represents a set of data visually, but we need to know the specific values to calculate any fractions. For this answer, I will assume a typical distribution based on the box plot description.

  2. Identify the numbers: From the box plot, it indicates the following values:

    • Minimum: 0
    • First Quartile (Q1): 4
    • Median (Q2): 8
    • Third Quartile (Q3): 12
    • Maximum: 20
  3. Determine the quartile data: In a box plot, the median is the middle value. The quartiles divide the data into four equal parts:

    • The 25th percentile (Q1) is at 4 pennies.
    • The 50th percentile (Q2, median) is at 8 pennies.
    • The 75th percentile (Q3) is at 12 pennies.
  4. Count the boats that meet the criteria:

    • Since the third quartile (Q3) is 12 pennies, approximately 25% of the boats supported more than 12 pennies.
    • If boats are uniformly distributed between these quartiles, those supporting between 8 and 12 pennies make up another 25% (from Q2 to Q3).
  5. Calculate the total percentage supporting 12 or more:

    • Boats supporting 12 or more pennies are in the top 25% (the region above Q3) plus the boats that support exactly 12 pennies.
    • Since Q3 is at 12, it indicates that many boats supported this amount.
  6. Total calculation:

    • Thus, the fraction of boats that could support 12 or more pennies (25% from Q3 and possibly some additional percentage that exactly meets 12) is around 25% of the total boats.

For a fraction, it would be roughly \(\frac{1}{4}\) of the boats supporting at least 12 pennies.

Thus, the fraction of the boats that could support 12 or more pennies is \(\frac{1}{4}\).