2)

$p=0,951$ $n=720$

$\mu =n\ast p=720\ast 0,951=684,72$
$\sigma =\sqrt{n\ast p\ast q}=\sqrt{720\ast 0,951\ast (1-0,951)}\approx 5,79$

Sigma Regel für 90%:
$r=1,64\sigma =1,64\ast 5,79\approx 9,49$
$P(684,72-9,49\le x\le 684,72+9,49)=P(675,23\le x\le 694,21)$

Sigma Regel für 95%:
$r=1,96\sigma =1,96\ast 5,79\approx 11,35$
$P(684,72-11,35\le x\le 684,72+11,35)=P(673,37\le x\le 696,07)$

Sigma Regel für 99%:
$r=2,58\sigma =2,58\ast 5,79\approx 14,94$
$P(684,72-14,94\le x\le 684,72+14,94)=P(669,78\le x\le 699,66)$

$p=0,85$ $n=720$

$\mu =n\ast p=720\ast 0,85=612$
$\sigma =\sqrt{n\ast p\ast q}=\sqrt{720\ast 0,85\ast (1-0,85)}\approx 9,58$

Sigma Regel für 90%:
$r=1,64\sigma =1,64\ast 9,58\approx 15,71$
$P(612-15,71\le x\le 612+15,71)=P(596,29\le x\le 627,71)$

Sigma Regel für 95%:
$r=1,96\sigma =1,96\ast 9,58\approx 18,78$
$P(612-18,78\le x\le 612+18,78)=P(593,22\le x\le 630,78)$

Sigma Regel für 99%:
$r=2,58\sigma =2,58\ast 9,58\approx 24,72$
$P(612-24,72\le x\le 612+24,72)=P(587,28\le x\le 636,72)$

$p=0,191$ $n=720$

$\mu =n\ast p=720\ast 0,191=137,52$
$\sigma =\sqrt{n\ast p\ast q}=\sqrt{720\ast 0,191\ast (1-0,191)}\approx 10,57$

Sigma Regel für 90%:
$r=1,64\sigma =1,64\ast 10,57\approx 17,33$
$P(137,52-17,33\le x\le 137,52+17,33)=P(120,19\le x\le 154,85)$

Sigma Regel für 95%:
$r=1,96\sigma =1,96\ast 10,57\approx 20,72$
$P(137,52-20,72\le x\le 137,52+20,72)=P(116,80\le x\le 158,24)$

Sigma Regel für 99%:
$r=2,58\sigma =2,58\ast 10,57\approx 27,27$
$P(137,52-27,27\le x\le 137,52+27,27)=P(110,25\le x\le 164,79)$

$p=0,258$ $n=720$

$\mu =n\ast p=720\ast 0,258=185,76$
$\sigma =\sqrt{n\ast p\ast q}=\sqrt{720\ast 0,258\ast (1-0,258)}\approx 11,75$

Sigma Regel für 90%:
$r=1,64\sigma =1,64\ast 11,75\approx 19,27$
$P(185,76-19,27\le x\le 185,76+19,27)=P(166,49\le x\le 205,03)$

Sigma Regel für 95%:
$r=1,96\sigma =1,96\ast 11,75\approx 23,03$
$P(185,76-23,03\le x\le 185,76+23,03)=P(162,73\le x\le 208,79)$

Sigma Regel für 99%:
$r=2,58\sigma =2,58\ast 11,75\approx 30,32$
$P(185,76-30,32\le x\le 185,76+30,32)=P(155,44\le x\le 216,08)$

$p=0,951$ $n=720$

90%-Intervall: $P(675,23\le x\le 694,21)$
$\approx binomcdf(720,0,951,694)-binomcdf(720,0,951,675)$
$\approx 0,8998$

95%-Intervall: $P(673,37\le x\le 696,07)$
$\approx binomcdf(720,0,951,696)-binomcdf(720,0,951,673)$
$\approx 0,9502$

99%-Intervall: $P(669,78\le x\le 699,66)$
$\approx binomcdf(720,0,951,699)-binomcdf(720,0,951,669)$
$\approx 0,9901$

$p=0,85$ $n=720$

90%-Intervall: $P(596,29\le x\le 627,71)$
$\approx binomcdf(720,0,85,627)-binomcdf(720,0,85,596)$
$\approx 0,8997$

95%-Intervall: $P(593,22\le x\le 630,78)$
$\approx binomcdf(720,0,85,630)-binomcdf(720,0,85,593)$
$\approx 0,9499$

99%-Intervall: $P(587,28\le x\le 636,72)$
$\approx binomcdf(720,0,85,636)-binomcdf(720,0,85,587)$
$\approx 0,9900$

$p=0,191$ $n=720$

90%-Intervall: $P(120,19\le x\le 154,85)$
$\approx binomcdf(720,0,191,154)-binomcdf(720,0,191,120)$
$\approx 0,9001$

95%-Intervall: $P(116,80\le x\le 158,24)$
$\approx binomcdf(720,0,191,158)-binomcdf(720,0,191,116)$
$\approx 0,9498$

99%-Intervall: $P(110,25\le x\le 164,79)$
$\approx binomcdf(720,0,191,164)-binomcdf(720,0,191,110)$
$\approx 0,9899$

$p=0,258$ $n=720$

90%-Intervall: $P(166,49\le x\le 205,03)$
$\approx binomcdf(720,0,258,205)-binomcdf(720,0,258,166)$
$\approx 0,8999$

95%-Intervall: $P(162,73\le x\le 208,79)$
$\approx binomcdf(720,0,258,208)-binomcdf(720,0,258,162)$
$\approx 0,9501$

99%-Intervall: $P(155,44\le x\le 216,08)$
$\approx binomcdf(720,0,258,216)-binomcdf(720,0,258,155)$

$\approx 0,9902$

4)

$\mu -r\le x\le \mu +r$
$n\ast p-1,64(\sqrt{n\ast p\ast q})\le x\le n\ast p+1,64(\sqrt{n\ast p\ast q})$
CAS (solve):
$11,2182\le x\le 24,7818$

$P(11,2182\le x\le 24,7818)$