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Консультация № 196811
25.10.2019, 16:06
0.00 руб.
25.10.2019, 18:57
0
3
1
Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос
. Фирма собирается приобрести партию из 10000 единиц некоторого товара. Из прошлого опыта известно, что 1% товаров данного типа имеет дефекты. Какова вероятность того, что в данной партии окажется от 950 до 1050 дефектных единиц товара?
Спасибо!
. Фирма собирается приобрести партию из 10000 единиц некоторого товара. Из прошлого опыта известно, что 1% товаров данного типа имеет дефекты. Какова вероятность того, что в данной партии окажется от 950 до 1050 дефектных единиц товара?
Спасибо!
Обсуждение
30.10.2019, 16:01
общий
это ответ
Здравствуйте, Женя!
Если некоторое случайное событие наступает с вероятностью p и не наступает с вероятностью q=1-p, то случайная величина X, равная числу событий при n испытаниях, имеет биномиальное распределение, для которого MX = np и DX = npq. Вероятность отклонения случайной величины от среднего значения можно оценить с помощью неравенства Чебышева
или
В данном случае n = 100000 единиц товара, p = 1% = 0.01, q = 1 - p = 0.99, MX = 100000[$183$]0.01 = 1000, DX = 100000[$183$]0.01[$183$]0.99 = 990, a = 1050 - 1000 = 1000 - 950 = 50 и
Для получения более точного значения можно использовать предельную интегральную теорему Муавра-Лапласа для биномиального распределения:
или
где [$934$] - функция Лапласа,
В данном случае n[sub]1[/sub] = 950, n[sub]2[/sub] = 1050,
и вероятность приближенно равна
Если некоторое случайное событие наступает с вероятностью p и не наступает с вероятностью q=1-p, то случайная величина X, равная числу событий при n испытаниях, имеет биномиальное распределение, для которого MX = np и DX = npq. Вероятность отклонения случайной величины от среднего значения можно оценить с помощью неравенства Чебышева
или
В данном случае n = 100000 единиц товара, p = 1% = 0.01, q = 1 - p = 0.99, MX = 100000[$183$]0.01 = 1000, DX = 100000[$183$]0.01[$183$]0.99 = 990, a = 1050 - 1000 = 1000 - 950 = 50 и
Для получения более точного значения можно использовать предельную интегральную теорему Муавра-Лапласа для биномиального распределения:
или
где [$934$] - функция Лапласа,
В данном случае n[sub]1[/sub] = 950, n[sub]2[/sub] = 1050,
и вероятность приближенно равна
5
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