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Консультация № 174084
09.11.2009, 09:10
0.00 руб.
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Здравствуйте! Имеется задачка по теории вероятностей следующего содержания:
Заданы среднее квадратическое отклонение СИГМА(х) нормально распределенной случайной величины Х, выборочная средняя х(сверху черточка), объем выборки n. Найти доверительные интервалы для оценки неизвестного математического ожидания M(x) с заданной надежностью V = 0.95.
СИГМА(х)=6, х(сверху черточка)=18.61, n=81.
Буду рад любой помощи в решении данной задачи. Вся надежда только на вас, уважаемые эксперты.
Заданы среднее квадратическое отклонение СИГМА(х) нормально распределенной случайной величины Х, выборочная средняя х(сверху черточка), объем выборки n. Найти доверительные интервалы для оценки неизвестного математического ожидания M(x) с заданной надежностью V = 0.95.
СИГМА(х)=6, х(сверху черточка)=18.61, n=81.
Буду рад любой помощи в решении данной задачи. Вся надежда только на вас, уважаемые эксперты.
Обсуждение
12.11.2009, 20:40
общий
это ответ
Здравствуйте, Quikk.
В данном случае доверительный интервал суть
(X‾ - tσ/√n; X‾ + tσ/√n), (1)
где t определяется из равенства
Ф0(t) = γ/2 или Ф(t) = (1 + γ)/2.
При заданном γ = 0,95 получаем Ф0(t) = 0,95/2 = 0,475. По таблице функции Лапласа находим t = 1,96. Подставляя найденное значение аргумента t вместе с заданными величинами в формулу (1), находим искомый доверительный интервал для MX:
(18,61 – 1,96 ∙ 6/√81; 18,61 + 1,96 ∙ 6/√81),
или
(17,30; 19,92).
Ответ: (17,30; 19,92).
С уважением.
В данном случае доверительный интервал суть
(X‾ - tσ/√n; X‾ + tσ/√n), (1)
где t определяется из равенства
Ф0(t) = γ/2 или Ф(t) = (1 + γ)/2.
При заданном γ = 0,95 получаем Ф0(t) = 0,95/2 = 0,475. По таблице функции Лапласа находим t = 1,96. Подставляя найденное значение аргумента t вместе с заданными величинами в формулу (1), находим искомый доверительный интервал для MX:
(18,61 – 1,96 ∙ 6/√81; 18,61 + 1,96 ∙ 6/√81),
или
(17,30; 19,92).
Ответ: (17,30; 19,92).
С уважением.
5
Огромное Вам спасибо!
Об авторе:
Facta loquuntur.
Facta loquuntur.
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