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小小苏 · 2020年02月25日

问一道题：NO.PZ2015120604000117

  1. CFA I
  2. Quantitative

问题如下：

A random sample is 100 CFA candidate's exam scoring. The mean of the scoring is 64. The standard deviation of the population scoring is 15 . The distribution is sopposed to be normal. The 95% confidence interval for the population mean should be:

选项：

A.

61.06 to 66.94.

B.

61.06 to 69.94.

C.

65.06 to 66.94.

解释：

A is correct.

Because the variance of the population is know and n ≥ 30,so The confidence interval is:

x¯ ± z α/2 (σ/ n )

z α/2 = z 0.025 =1.96

64 ± 1.96(15/10) = 64 ± 2.94 = 61.06 to 66.94.

如果这道题给的不是95%，那如何查Z表呢？在Z表中没有找到这个数呢

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1 个答案

星星_品职助教 · 2020年02月25日

同学你好，

置信区间是一定会给的，其实Z表的查表过程没啥意义，因为对应的值都让背过了。

Z表中给的是概率，查表的过程是根据95%的置信“区间”，得到单侧面积均为2.5%。然后就可以对应面积0.025查到-1.96，或者（更常用）根据右侧面积2.5%得到右左侧面积和为0.975，对应查到+1.96.



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