the following histograms each represent binomial distributions. each distribution has the same number of trials n but different probabilities of success p.

match $p = 0.4$, $p = 0.5$, $p = 0.6$ with the correct graph.

a. (a) $p = 0.6$, (b) $p = 0.5$, (c) $p = 0.4$
b. (a) $p = 0.5$, (b) $p = 0.6$, (c) $p = 0.4$
c. (a) $p = 0.6$, (b) $p = 0.4$, (c) $p = 0.5$
d. (a) $p = 0.4$, (b) $p = 0.6$, (c) $p = 0.5$
e. (a) $p = 0.4$, (b) $p = 0.5$, (c) $p = 0.6$
f. (a) $p = 0.5$, (b) $p = 0.4$, (c) $p = 0.6$

Question

the following histograms each represent binomial distributions. each distribution has the same number of trials n but different probabilities of success p.

match $p = 0.4$, $p = 0.5$, $p = 0.6$ with the correct graph.

a. (a) $p = 0.6$, (b) $p = 0.5$, (c) $p = 0.4$
b. (a) $p = 0.5$, (b) $p = 0.6$, (c) $p = 0.4$
c. (a) $p = 0.6$, (b) $p = 0.4$, (c) $p = 0.5$
d. (a) $p = 0.4$, (b) $p = 0.6$, (c) $p = 0.5$
e. (a) $p = 0.4$, (b) $p = 0.5$, (c) $p = 0.6$
f. (a) $p = 0.5$, (b) $p = 0.4$, (c) $p = 0.6$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Binomial Distribution Symmetry", "Binomial Parameter Matching" ], "new_concepts": [], "current_concepts": [ "Binomial Distribution Symmetry", "Binomial Parameter Matching" ] } ## Analyze distribution symmetry and skewness $$ \begin{aligned} &\text{For a binomial distribution with } n = 4:\ &p = 0.5 \implies \text{Symmetric distribution around the mean } \mu = n \cdot p = 2.\ &p < 0.5 \implies \text{Right-skewed (skewed to the right, peak shifted left)}.\ &p > 0.5 \implies \text{Left-skewed (skewed to the left, peak shifted right)}. \end{aligned} $$ ## Match parameters to graphs $$ \begin{aligned} &\text{Graph (a): Peak is at } x = 1 \text{ and } x = 2 \text{ (shifted left, right-skewed)} \implies p = 0.4.\ &\text{Graph (b): Peak is at } x = 2 \text{ and } x = 3 \text{ (shifted right, left-skewed)} \implies p = 0.6.\ &\text{Graph (c): Perfectly symmetric about } x = 2 \implies p = 0.5. \end{aligned} $$ ## Identify the correct option $$ \text{Matching: (a) } p = 0.4, \text{ (b) } p = 0.6, \text{ (c) } p = 0.5 \implies \text{Option D}. $$

A. (a) $p = 0.6$, (b) $p = 0.5$, (c) $p = 0.4$

B. (a) $p = 0.5$, (b) $p = 0.6$, (c) $p = 0.4$

C. (a) $p = 0.6$, (b) $p = 0.4$, (c) $p = 0.5$

D. (a) $p = 0.4$, (b) $p = 0.6$, (c) $p = 0.5$

E. (a) $p = 0.4$, (b) $p = 0.5$, (c) $p = 0.6$

F. (a) $p = 0.5$, (b) $p = 0.4$, (c) $p = 0.6$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Statistics", "Binomial Parameter Matching" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Analyze distribution symmetry and skewness

Match parameters to graphs

Identify the correct option

Answer: