// Numbas version: exam_results_page_options {"name": "Alex's copy of Binomial (practice of formula)", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Alex's copy of Binomial (practice of formula)", "variablesTest": {"maxRuns": 100, "condition": ""}, "extensions": ["stats"], "functions": {}, "ungrouped_variables": ["w", "ans1", "ans2", "n", "p", "v3", "v4", "tol", "x2", "x1", "tans1", "tans2"], "advice": "
a)
\\[\\simplify[std,!otherNumbers]{P(X = {x1}) = {n}! / ({n -x1}! * {x1}!) * {p} ^ {x1} * (1 -{p}) ^ {n -x1}} = \\var{ans1}\\]
to 3 decimal places.
\nb)
\nWe have:
\n\\[ \\begin{eqnarray*} F_X (\\var{x2}) &=& P(X \\le \\var{x2}) =\\simplify[std]{ P(X = 0) + P(X = 1) + P(X = 2) + {v3} * P(X = 3) + {v4} * P(X = 4)}\\\\ &=& \\simplify[unitFactor,zeroTerm,zeroFactor]{(1 -{p}) ^ {n} + {n} * (1 -{p}) ^ {n -1} * {p} + {(n * (n -1)) / 2} * (1 -{p}) ^ {n -2} * {p} ^ 2 + {v3} * {Comb(n , 3)} * (1 -{p}) ^ {n -3} * {p} ^ 3 + {v4} * {Comb(n , 4)} * (1 -{p}) ^ {n -4} * {p} ^ 4}\\\\ &=&\\var{ans2} \\end{eqnarray*} \\]
to 3 decimal places.
Answer the following questions on the Binomial Distribution.
\nSuppose \\[X \\sim \\operatorname{Binomial}(\\var{n},\\var{p}),\\]
\nthat is $n=\\var{n}$ and $p=\\var{p}$.
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\nrebelmaths
", "licence": "Creative Commons Attribution 4.0 International"}, "question_groups": [{"pickQuestions": 0, "name": "", "pickingStrategy": "all-ordered", "questions": []}], "contributors": [{"name": "Alex Van den Hof", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1273/"}]}]}], "contributors": [{"name": "Alex Van den Hof", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1273/"}]}