> x=c(10,20,30,40,50,60,70,80)
> z=(x-38.8)/22.3
> z
[1] -1.29147982 -0.84304933 -0.39461883  0.05381166  0.50224215  0.95067265
[7]  1.39910314  1.84753363
> Fz=pnorm(z)
> Fz
[1] 0.09826867 0.19960043 0.34656211 0.52145739 0.69225140 0.82911471
[7] 0.91910897 0.96766508
> a
[1] 0.1996004 0.3465621 0.5214574 0.6922514 0.8291147 0.9191090 0.9676651
[8] 1.0000000
> a-Fz
[1] 0.10133175 0.14696168 0.17489528 0.17079401 0.13686331 0.08999426
[7] 0.04855611 0.03233492
> E=c(88*Fz[1],88*(a-Fz))
> E
[1]  8.647643  8.917194 12.932628 15.390785 15.029873 12.043971  7.919495
[8]  4.272938  2.845473
> e=c(E[1:7],E[8]+E[9])
> e
[1]  8.647643  8.917194 12.932628 15.390785 15.029873 12.043971  7.919495
[8]  7.118410
> o=c(4, 8, 20,19,12,7,9,9)
> xx=sum((o-e)^2/e)
> xx
[1] 10.66869
> df=length(e)-1-2
> df
[1] 5
> qchisq(.95,5)
[1] 11.0705
> qchisq(.9,5)
[1] 9.236357
> qchisq(.95,df)
[1] 11.0705
> qchisq(.9,df)
[1] 9.236357