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Консультация № 160284
12.02.2009, 12:37
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Помогите решить задачку... по теории вероятности...
Средний процент выполнения плана некоторыми предприятиями составляет 106%, среднее квадратическое отклонение 9%. Полагая, что выполнение плана этой группой предприятий подчиняется нормальному закону, определить процент предприятий, не выполняющих план.
Спасибо.
Средний процент выполнения плана некоторыми предприятиями составляет 106%, среднее квадратическое отклонение 9%. Полагая, что выполнение плана этой группой предприятий подчиняется нормальному закону, определить процент предприятий, не выполняющих план.
Спасибо.
Обсуждение
Неизвестный
12.02.2009, 14:44
общий
это ответ
Здравствуйте, Бондаренко Ольга Ивановна!
В вашей задаче требуется найти вероятность того, что нормально распределенная случайная величина X (процент выполнения плана), у которой мат.ожидание равно a=106, и ср.кв.отклонение s=9, примет значение от 0 до 100.
Используем формулу:
P(c<X<d) = 1/2[Ф((d-a)/s)-Ф((c-a)/s)], где Ф(t) - функция Лапласа, ее значения ищутся по соответствующим таблицам (например, здесь http://stratum.ac.ru/textbooks/modelir/lection34-01.html)
(d-a)/s = (100-106)/9 = -2/3, Ф(-0.67)=-Ф(0,67)=-0,4972
(c-a)/s = (0-106)/9 = -106/9, Ф(-11,8) = -1 (Ф(t)=1 для всех t>5)
Искомая вероятнось равна 1/2[-0,4972-(-1)] = 0,2514
В вашей задаче требуется найти вероятность того, что нормально распределенная случайная величина X (процент выполнения плана), у которой мат.ожидание равно a=106, и ср.кв.отклонение s=9, примет значение от 0 до 100.
Используем формулу:
P(c<X<d) = 1/2[Ф((d-a)/s)-Ф((c-a)/s)], где Ф(t) - функция Лапласа, ее значения ищутся по соответствующим таблицам (например, здесь http://stratum.ac.ru/textbooks/modelir/lection34-01.html)
(d-a)/s = (100-106)/9 = -2/3, Ф(-0.67)=-Ф(0,67)=-0,4972
(c-a)/s = (0-106)/9 = -106/9, Ф(-11,8) = -1 (Ф(t)=1 для всех t>5)
Искомая вероятнось равна 1/2[-0,4972-(-1)] = 0,2514
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