match n = 4, n = 8, n = 12 with the correct graph. each histogram shown below represents part of a binomial distribution. each distribution has the same probability of success p but different numbers of trials n.

histogram (b) has the number of trials n = 4
histogram (c) has the number of trials n =

Question

match n = 4, n = 8, n = 12 with the correct graph. each histogram shown below represents part of a binomial distribution. each distribution has the same probability of success p but different numbers of trials n.

histogram (b) has the number of trials n = 4
histogram (c) has the number of trials n =

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Binomial Parameter Matching" ], "new_concepts": [], "current_concepts": [ "Binomial Parameter Matching", "Binomial Distribution Symmetry" ] } ## Identify the maximum possible value of $x$ for each histogram $$ \begin{aligned} &\text{For (b): } P(x) > 0 \text{ only for } x \le 4 \implies n = 4\ &\text{For (c): } P(x) > 0 \text{ only for } x \le 8 \implies n = 8\ &\text{For (a): } P(x) > 0 \text{ only for } x \le 12 \implies n = 12 \end{aligned} $$ ## Match the histograms to the given values of $n$ $$ \begin{aligned} &\text{Histogram (b)} \implies n = 4\ &\text{Histogram (c)} \implies n = 8\ &\text{Histogram (a)} \implies n = 12 \end{aligned} $$ ## Question 1 Histogram (b) has the number of trials n = 4 ## Question 2 Histogram (c) has the number of trials n = 8 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Binomial Parameter Matching" ] }

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Question

Explanation:

Identify the maximum possible value of \(x\) for each histogram

Match the histograms to the given values of \(n\)

Answer:

Question 1

Question 2