a stem-and-leaf plot for the number of touchdowns scored by all division 1a football teams is shown below. complete parts (a) through (c).

\begin{array}{r|l}
1 & 3\; 4\; 5\; 7\; 8\; 8 \quad \text{key: } 1|5 = 15 \\
2 & 0\; 1\; 2\; 2\; 3\; 4\; 5\; 7\; 8\; 8\; 9 \\
3 & 0\; 0\; 1\; 1\; 1\; 2\; 2\; 3\; 3\; 4\; 4\; 5\; 5\; 7\; 7\; 7\; 8\; 9 \\
4 & 0\; 0\; 1\; 2\; 2\; 3\; 4\; 5\; 5\; 5\; 5\; 6\; 7\; 8\; 8\; 9 \\
5 & 0\; 2\; 3\; 5\; 5\; 7\; 8 \\
6 & 1\; 3\; 6\; 7 \\
7 & \\
8 & 7
\end{array}

(a) if a team is selected at random, find the probability the team scored at least 32 touchdowns.
(round to three decimal places as needed.)

Question

a stem-and-leaf plot for the number of touchdowns scored by all division 1a football teams is shown below. complete parts (a) through (c).

\begin{array}{r|l}
1 & 3\; 4\; 5\; 7\; 8\; 8 \quad \text{key: } 1|5 = 15 \\
2 & 0\; 1\; 2\; 2\; 3\; 4\; 5\; 7\; 8\; 8\; 9 \\
3 & 0\; 0\; 1\; 1\; 1\; 2\; 2\; 3\; 3\; 4\; 4\; 5\; 5\; 7\; 7\; 7\; 8\; 9 \\
4 & 0\; 0\; 1\; 2\; 2\; 3\; 4\; 5\; 5\; 5\; 5\; 6\; 7\; 8\; 8\; 9 \\
5 & 0\; 2\; 3\; 5\; 5\; 7\; 8 \\
6 & 1\; 3\; 6\; 7 \\
7 &  \\
8 & 7
\end{array}

(a) if a team is selected at random, find the probability the team scored at least 32 touchdowns.
(round to three decimal places as needed.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Stem-and-Leaf Plot", "Classical Probability" ], "new_concepts": [], "current_concepts": [ "Stem-and-Leaf Plot", "Classical Probability" ] } ## Count total observations Using the *Stem-and-Leaf Plot* knowledge point $$ \begin{aligned} &\text{Row 1 (1|): } 3, 4, 5, 7, 8, 8 \implies 6 \text{ values} \ &\text{Row 2 (2|): } 0, 1, 2, 2, 3, 4, 5, 7, 8, 8, 9 \implies 11 \text{ values} \ &\text{Row 3 (3|): } 0, 0, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 7, 7, 7, 8, 9 \implies 18 \text{ values} \ &\text{Row 4 (4|): } 0, 0, 1, 2, 2, 3, 4, 5, 5, 5, 5, 6, 7, 8, 8, 9 \implies 16 \text{ values} \ &\text{Row 5 (5|): } 0, 2, 3, 5, 5, 7, 8 \implies 7 \text{ values} \ &\text{Row 6 (6|): } 1, 3, 6, 7 \implies 4 \text{ values} \ &\text{Row 7 (7|): } \text{No leaves} \implies 0 \text{ values} \ &\text{Row 8 (8|): } 7 \implies 1 \text{ value} \ &N = 6 + 11 + 18 + 16 + 7 + 4 + 0 + 1 = 63 \end{aligned} $$ ## Count favorable outcomes Using the *Stem-and-Leaf Plot* knowledge point $$ \begin{aligned} &\text{Values } \ge 32: \ &\text{Row 3 (3|): } 32, 32, 33, 33, 34, 34, 35, 35, 37, 37, 37, 38, 39 \implies 13 \text{ values} \ &\text{Row 4 (4|): } \text{All } 16 \text{ values} \ &\text{Row 5 (5|): } \text{All } 7 \text{ values} \ &\text{Row 6 (6|): } \text{All } 4 \text{ values} \ &\text{Row 8 (8|): } \text{All } 1 \text{ value} \ &f = 13 + 16 + 7 + 4 + 1 = 41 \end{aligned} $$ ## Calculate probability Using the *Classical Probability* knowledge point $$ \begin{aligned} &P(\text{at least } 32) = \frac{f}{N} = \frac{41}{63} \approx 0.65079 \end{aligned} $$ ## Round to three decimal places Using the *Classical Probability* knowledge point $$ \begin{aligned} &P(\text{at least } 32) \approx 0.651 \end{aligned} $$ (a) If a team is selected at random, find the probability the team scored at least 32 touchdowns. 0.651 (Round to three decimal places as needed.) { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Classical Probability" ] }

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QUESTION IMAGE

Question

Explanation:

Count total observations

Count favorable outcomes

Calculate probability

Round to three decimal places

Answer: