What is the probability that a long jump participant chosen at random from the competition will have jumped at least 75 inches?
Understand the Problem
The question asks us to find the probability that a randomly chosen participant jumped at least 75 inches, based on the given stem-and-leaf plot data.
Answer
$\frac{6}{10}$
Answer for screen readers
$\frac{6}{10}$
Steps to Solve
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Interpret the stem-and-leaf plot The stem-and-leaf plot represents the jump distances. Given the key 7 | 3 = 73 inches, we can decode each jump distance. The stems are the tens digits, and the leaves are the units digits.
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List all the jump distances From the stem-and-leaf plot, the distances are: 68, 69, 71, 74, 77, 78, 79, 80, 81, 82.
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Count the total number of participants There are 10 participants in total.
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Count the number of participants who jumped at least 75 inches The participants who jumped at least 75 inches are those with distances: 77, 78, 79, 80, 81, 82. So there are 6 such participants.
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Calculate the probability The probability is the number of participants who jumped at least 75 inches divided by the total number of participants: $P(\text{at least 75 inches}) = \frac{\text{Number of participants who jumped at least 75 inches}}{\text{Total number of participants}} = \frac{6}{10}$.
$\frac{6}{10}$
More Information
The probability that a randomly chosen participant jumped at least 75 inches is $\frac{6}{10}$, which can be simplified to $\frac{3}{5}$.
Tips
A common mistake is misinterpreting the stem-and-leaf plot or miscounting the number of participants who jumped at least 75 inches. Another mistake could arise by not simplifying the fraction.
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