# 麻煩幫忙提示點寫一題統計問題!!

A public opinion poll in southern California was conducted to determine whether southern Californians are prepared for the ' big earthquake' that experts predict will devastate the region sometime in the next 50 years. It was learned that '60% have not secured objects in their homes that might fall and cause injury and damage during a temblor.' In a random sample of n = 864 southern Californians, let X equal the number who '' have not secured objects in their homes." Find P(496≦X≦548), approximately.

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### 1 個解答

• 10 年前
最佳解答

大意:

一個有關是否做防震準備的調查.

假設群體(加州民眾)有60%未把家裡的東西弄得安全(免得房子搖晃時

掉落傷人), 若樣本大小是 n=864, X 代表樣本中未把家裡東西弄得安

全的人數. 問 X 介於 496 和 548 之間的機率.

正確機率是依二項分布計算, 但 n 大, 可用常態近似.

簡單的練習.

2011-03-31 22:16:52 補充：

大意:

一個有關是否做防震準備的調查.

假設群體(加州民眾)有60%未把家裡的東西弄得安全(免得房子搖晃時

掉落傷人), 若樣本大小是 n=864, X 代表樣本中未把家裡東西弄得安

全的人數. 問 X 介於 496 和 548 之間的機率.

正確機率是依二項分布計算, 但 n 大, 可用常態近似.

由於 n 相當大, 有沒有做連續性校正應該影響很小. 不過習慣上我仍

會考慮, 所以 P[496≦X≦548] = P[495.5<X<548.5].

2011-04-01 00:45:25 補充：

E[X] = np = 864*0.6 = 518.4

Var(X) = np(1-p) = 864*0.6*0.4 = 207.36 = 14.4^2

SD(X) = 14.4