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國小教甄|英語英語106 年第 40 題單選題

Figure (A) demonstrates a normal distribution of English midterm performance of Eagle class students. The statistical data shows that students' mean score is 70 points, with a standard deviation of 10 points. There are 30 students in Eagle class. Based on the data and the graph, which of the following statement is TRUE?

Aw=55, x=60, y=80, z=90
BTwenty-five students in Eagle Class scored above 60 and passed the English midterm exam.正確答案
CStudents who scored within the 90-100 range were as many as students who scored within the 50-60 range.
DAccording to the graph, we are 95 percent certain that individual student's actual score will be within one standard error of 70 points.
答案與詳解
B
正確答案
根據常態分佈特性,高於負一個標準差(60分)的人數約佔84%,30人的84%約為25人。

逐選項解析

Aw=55, x=60, y=80, z=90✕ 錯誤
常態分佈圖上的刻度應為平均數加減標準差的整數倍(如50、60、80、90),w=55不符合標準差為10的倍數關係。
BTwenty-five students in Eagle Class scored above 60 and passed the English midterm exam.✓ 正確
CStudents who scored within the 90-100 range were as many as students who scored within the 50-60 range.✕ 錯誤
90至100分屬於+2SD至+3SD的區間(約佔2.35%),而50至60分屬於-2SD至-1SD的區間(約佔13.5%),兩者比例與人數不相同。
DAccording to the graph, we are 95 percent certain that individual student's actual score will be within one standard error of 70 points.✕ 錯誤

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