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Консультация № 174360
19.11.2009, 11:01
0.00 руб.
0
1
1
Автоматическая штамповка клемм для предохранителей дает 10% отклонений от принятого стандарта. Сколько стандартных клемм следует ожидать с вероятностью 0,0587 среди 400 клемм?
Заранее спасибо.
Заранее спасибо.
Обсуждение
24.11.2009, 15:56
общий
это ответ
Здравствуйте, Александров Анатолий Олегович.
1. Дано n=400, p=0.9, q=1-p=1-0.9=0.1
2. Так как n велико, воспользуемся локальной теоремой Лапласа. Pn(k)=1/√(n*p*q)*φ(x)=0.0587
3. √(n*p*q) = √(400*0.9*0.1) = 6
4. φ(x)= Pn(k)*√(n*p*q)=0.0587*6=0.3522
5. По таблице значений функции φ(x)=1/√(2*π)*e^(-x^2/2) находим, что φ(x)= 0.3521 соответствует x=0.5. Принимаем x=0.5
6. x=(k-np)/ √(n*p*q) -> k=np+x*√(n*p*q)=400*0.9+0.5*6=363
Ответ: следует ожидать 363 стандартных клеммы
1. Дано n=400, p=0.9, q=1-p=1-0.9=0.1
2. Так как n велико, воспользуемся локальной теоремой Лапласа. Pn(k)=1/√(n*p*q)*φ(x)=0.0587
3. √(n*p*q) = √(400*0.9*0.1) = 6
4. φ(x)= Pn(k)*√(n*p*q)=0.0587*6=0.3522
5. По таблице значений функции φ(x)=1/√(2*π)*e^(-x^2/2) находим, что φ(x)= 0.3521 соответствует x=0.5. Принимаем x=0.5
6. x=(k-np)/ √(n*p*q) -> k=np+x*√(n*p*q)=400*0.9+0.5*6=363
Ответ: следует ожидать 363 стандартных клеммы
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