请求帮助

Doris1930

A certain characteristic in a large population has a distribution that is symmetric about the mean
                m.  If 68 percent of the distribution lies within one standard deviation
                d of the mean, what percent of the distribution is less than m +
                    d ?

A.     16%

B.     32%

C.     48%

D.     84%

E.      92%

答案是   D

看了半天没明白是什么意思，也无从下手

请好心人帮忙解答一下，我将感激不尽.......

sangyeyoyo

大学高数学的，考试也考这道了。。。。

因为it is symmetric about m, 也就是说, data less than m is 50% and data greater than m is also 50%. 呈对称图像，不会画图，不好意思。。。

所以  each of the area from m to m+d and to m-d would be 34% (68/2=34%.)

m+d to m = 34%
data less than m is 50%
thus m+ d = 50 + 34 = 84%

gusaiyu

你看成正态分布不就好了，m-d 与m+d之间是68%，小于m的是50%，那明显小于m+d的就是50%+34%

bloodyawful

已知  X ~ N (µ,σ^2)

则
                            P{ X ≤ µ+σ } ≈ 84.13%

bloodyawful

Normal Distribution (wikipedia)

range	fraction in range	expected frequency outside range	approximate frequency for daily event
μ ± 1σ	0.682689492137	1 in 3	weekly
μ ± 2σ	0.954499736104	1 in 22	monthly
μ ± 3σ	0.997300203937	1 in 370	yearly
μ ± 4σ	0.999936657516	1 in 15,787	every 60 years (once in a lifetime)
μ ± 5σ	0.999999426697	1 in 1,744,278	every 5,000 years (once in history)
μ ± 6σ	0.999999998027	1 in 506,842,372	every 1.5 million years (essentially never)

zσ	percentage
1σ	68.2689492%
1.645σ	90%
1.960σ	95%
2σ	95.4499736%
2.576σ	99%
3σ	99.7300204%
3.2906σ	99.9%
4σ	99.993666%
5σ	99.99994267%
6σ	99.9999998027%
7σ	99.9999999997440%

[此贴子已经被作者于2009-3-30 12:20:54编辑过]

Doris1930

原来是这样,总算是搞明白了,谢谢大家的帮助!!!