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Консультация № 174451
22.11.2009, 23:01
0.00 руб.
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Здравствуйте, уважаемые эксперты!
Заранее спасибо!
Считается, что изделие – высшего качества, если отклонение его размеров от номинальных не превосходит по абсолютной величине 3,6 мм. Случайные отклонения размера изделия от номинального подчиняются нормальному закону со средним квадратичным отклонением, равным 3 мм. Систематические отклонения отсутствуют. Определить среднее число изделий высшего качества среди 100 изготовленных.
Заранее спасибо!
Считается, что изделие – высшего качества, если отклонение его размеров от номинальных не превосходит по абсолютной величине 3,6 мм. Случайные отклонения размера изделия от номинального подчиняются нормальному закону со средним квадратичным отклонением, равным 3 мм. Систематические отклонения отсутствуют. Определить среднее число изделий высшего качества среди 100 изготовленных.
Обсуждение
28.08.2022, 15:38
общий
это ответ
Здравствуйте, Сергей Юриевич!
Случайная величина
-- отклонение размера изделия от номинального -- подчиняется нормальному закону распределения с параметрами 
(поскольку систематические отклонения отсутствуют), 
Вычислим вероятность того, что изготовленное изделие имеет высшее качество, по формуле 
где 
-- нормированная функция Лапласа [1, с. 56, 102]. При 
из указанной формулы получим
Тогда
-- среднее число изделий высшего качества среди ста изготовленных.
Литература
1 Письменный Д. Т. Конспект лекций по теории вероятностей, математической статистике и случайным процессам. -- М.: Айрис-пресс, 2008.
Случайная величина
-- отклонение размера изделия от номинального -- подчиняется нормальному закону распределения с параметрами (поскольку систематические отклонения отсутствуют), Вычислим вероятность того, что изготовленное изделие имеет высшее качество, по формуле где -- нормированная функция Лапласа [1, с. 56, 102]. При из указанной формулы получимТогда
-- среднее число изделий высшего качества среди ста изготовленных.Литература
1 Письменный Д. Т. Конспект лекций по теории вероятностей, математической статистике и случайным процессам. -- М.: Айрис-пресс, 2008.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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