esimerkkejä ratkaisuista
https://peda.net/id/b4595e02dd2
2018-10-31T18:26:22+02:00
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<div class="license">Tämän sivun lisenssi <a rel="license" href="https://peda.net/info">Peda.net-yleislisenssi</a></div>
406.
https://peda.net/id/7d4867a65f6
2022-11-08T15:03:42+02:00
<a href="https://peda.net/p/leena.k./mab-8/4tp/4l/er/4063/nayttokuva-2022-11-08-150125.jpg#top" title="Näyttökuva 2022-11-08 150125.jpg"><img src="https://peda.net/p/leena.k./mab-8/4tp/4l/er/4063/nayttokuva-2022-11-08-150125.jpg:file/photo/75cde81d21cd887c86ab2529cf3435f941f20e19/N%C3%A4ytt%C3%B6kuva%202022-11-08%20150125.jpg" alt="" title="Näyttökuva 2022-11-08 150125.jpg" class="inline" loading="lazy"/></a>
2022-11-08T15:01:41+02:00
402.
https://peda.net/id/f8b8694edd2
2018-10-31T18:35:27+02:00
<a href="https://peda.net/p/leena.k./mab-8/4tp/4l/er/402/virhemarg-kuva-png2#top" title="virhemarg.kuva.PNG"><img src="https://peda.net/p/leena.k./mab-8/4tp/4l/er/402/virhemarg-kuva-png2:file/photo/8a18faaba9f6dc3282d9788487230ab0ac4b7cbe/virhemarg.kuva.PNG" alt="" title="virhemarg.kuva.PNG" class="inline" loading="lazy"/></a><br/>
<a href="https://peda.net/p/leena.k./mab-8/4tp/4l/er/402/403-png#top" title="403..PNG"><img src="https://peda.net/p/leena.k./mab-8/4tp/4l/er/402/403-png:file/photo/d49149c79625b8db0777630bcd6ed79284904485/403..PNG" alt="" title="403..PNG" class="inline" loading="lazy"/></a>
2018-10-31T18:28:17+02:00
404.
https://peda.net/id/4e2169e8dd2
2022-11-03T10:48:56+02:00
<img src="https://math-demo.abitti.fi/math.svg?latex=%5Coverline%7Bx%7D%3D33%7B%2C%7D9%5C%20cm" alt="\overline{x}=33{,}9\ cm"/><br/>
<img src="https://math-demo.abitti.fi/math.svg?latex=s%3D1%7B%2C%7D2%5C%20cm" alt="s=1{,}2\ cm"/>
<div><img src="https://math-demo.abitti.fi/math.svg?latex=n%3D4%5C%20kpl" alt="n=4\ kpl"/><br/>
<br/>
a)<br/>
<br/>
<img src="https://math-demo.abitti.fi/math.svg?latex=s_%7B%5Coverline%7Bx%7D%7D%3D%5Cfrac%7Bs%7D%7B%5Csqrt%7Bn%7D%7D%3D%5Cfrac%7B1%7B%2C%7D2%7D%7B%5Csqrt%7B4%7D%7D%3D0%7B%2C%7D6" alt="s_{\overline{x}}=\frac{s}{\sqrt{n}}=\frac{1{,}2}{\sqrt{4}}=0{,}6"/><br/>
<br/>
Vastaus : 0,6</div>
<br/>
<br/>
<br/>
<a href="https://peda.net/p/leena.k./mab-8/4tp/4l/er/404/404a-png#top" title="404a..PNG"><img src="https://peda.net/p/leena.k./mab-8/4tp/4l/er/404/404a-png:file/photo/196a7ce8d373ff76212fe190e350aa31fb17995f/404a..PNG" alt="" title="404a..PNG" class="inline" loading="lazy"/></a><br/>
<br/>
<a href="https://peda.net/p/leena.k./mab-8/4tp/4l/er/404/404b-png#top" title="404b.PNG"><img src="https://peda.net/p/leena.k./mab-8/4tp/4l/er/404/404b-png:file/photo/14fb1ef842ab040517db3d6553d64aa60aa14e70/404b.PNG" alt="" title="404b.PNG" class="inline" loading="lazy"/></a>
2018-10-31T18:37:49+02:00
405.
https://peda.net/id/a703311e413
2021-11-09T10:25:52+02:00
[[$ \left[ \bar{x}-2,58\dfrac{s}{\sqrt{n}};\ \bar{x}+2,58\dfrac{s}{\sqrt{n}} \right] $]]<br/>
<br/>
<br/>
<br/>
<div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Coverline%7Bx%7D%3D523%5C%20cm" alt="\overline{x}=523\ cm"/><br/>
<img src="https://math-demo.abitti.fi/math.svg?latex=n%3D60" alt="n=60"/></div>
<br/>
<img src="https://math-demo.abitti.fi/math.svg?latex=s%3D120" alt="s=120"/><br/>
<div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%5B523-2%7B%2C%7D58%5Cfrac%7B120%7D%7B%5Csqrt%7B60%7D%7D%3B%5C%20523%2B2%7B%2C%7D58%5Cfrac%7B120%7D%7B%5Csqrt%7B60%7D%7D%5Cright%5D%3D" alt="\left[523-2{,}58\frac{120}{\sqrt{60}};\ 523+2{,}58\frac{120}{\sqrt{60}}\right]="/><br/>
<span><br/>
</span></div>
<strong class="editor red"><span>Pyöristys pitää luottamusvälissä aina tehdä kauemmas keskiarvosta, joten luottamusväli on kolmen merkitsevän numeron tarkkuudella</span></strong><br/>
<br/>
<img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%5B492%7B%2C%7D635...%5C%20%3B%5C%20553%7B%2C%7D364...%5Cright%5D%5Capprox%5Cleft%5B492%5C%20%3B%5C%20554%5Cright%5D" alt="\left[492{,}635...\ ;\ 553{,}364...\right]\approx\left[492\ ;\ 554\right]"/><br/>
<br/>
V: <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%5B492%5C%20%3B%5C%20554%5Cright%5D" alt="\left[492\ ;\ 554\right]"/>
2021-11-09T10:25:52+02:00
405.
https://peda.net/id/a872f484dd2
2019-09-12T12:17:16+03:00
<a href="https://peda.net/p/leena.k./mab-8/4tp/4l/er/405/405-png#top" title="405.PNG"><img src="https://peda.net/p/leena.k./mab-8/4tp/4l/er/405/405-png:file/photo/6b52229404aa7acd4f8c04682267b507be921a37/405.PNG" alt="" title="405.PNG" class="inline" loading="lazy"/></a><br/>
<strong class="editor red">Kaava löytyy MAOL:sta. <br/>
</strong><br/>
Ratkaistuna sähköisesti:<br/>
<strong class="editor red"><br/>
</strong><a href="https://peda.net/p/leena.k./mab-8/4tp/4l/er/405/t4s#top" title="teht 405 sähköisesti.jpg"><img src="https://peda.net/p/leena.k./mab-8/4tp/4l/er/405/t4s:file/photo/f76fdb1d77f68068301f46e4ec312c1a1d420bde/teht%20405%20s%C3%A4hk%C3%B6isesti.jpg" alt="" title="teht 405 sähköisesti.jpg" class="inline" loading="lazy"/></a>
2018-10-31T18:40:21+02:00
406.
https://peda.net/id/d09351e8413
2022-11-07T07:29:14+02:00
n= 302<br/>
26 kpl käytti nikotiinivalmistetta<br/>
<br/>
<img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%5B%5Chat%7Bp%7D-1%7B%2C%7D96s%3B%5C%20%5Chat%7Bp%7D%2B1%7B%2C%7D96s%5Cright%5D%5C%20Kaava%5C%20MAOL%3Assa!" alt="\left[\hat{p}-1{,}96s;\ \hat{p}+1{,}96s\right]\ Kaava\ MAOL:ssa!"/> <strong class="editor red">Huom! Maolin kaavassa eri merkintä, kuin oppikirjassa.</strong><br/>
<br/>
<img src="https://math-demo.abitti.fi/math.svg?latex=s%3D%5Csqrt%7B%5Cfrac%7B%5Chat%7Bp%7D(1-%5Chat%7Bp%7D)%7D%7Bn%7D%7D%3D%5C%20%5C%20Kaava%5C%20MAOL%3Assa!" alt="s=\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=\ \ Kaava\ MAOL:ssa!"/><br/>
<br/>
Todennäköisyys, että otoksessa oleva käyttää nikotiinivalmistetta on siis<br/>
<img src="https://math-demo.abitti.fi/math.svg?latex=p%3D%5Cfrac%7B26%7D%7B302%7D%3D0%7B%2C%7D08609271523178807947" alt="p=\frac{26}{302}=0{,}08609271523178807947"/><br/>
<br/>
<img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%5B%5Chat%7Bp%7D-1%7B%2C%7D96s%3B%5C%20%5Chat%7Bp%7D%2B1%7B%2C%7D96s%5Cright%5D" alt="\left[\hat{p}-1{,}96s;\ \hat{p}+1{,}96s\right]"/><br/>
<div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%5B0%7B%2C%7D08609271523178807947-1%7B%2C%7D96s%5C%20%3B%5C%200%7B%2C%7D08609271523178807947%2B1%7B%2C%7D96s%5Cright%5D" alt="\left[0{,}08609271523178807947-1{,}96s\ ;\ 0{,}08609271523178807947+1{,}96s\right]"/> <strong class="editor red">Pitää laske s!</strong></div>
<br/>
<img src="https://math-demo.abitti.fi/math.svg?latex=s%3D%5Csqrt%7B%5Cfrac%7B%5Chat%7Bp%7D(1-%5Chat%7Bp%7D)%7D%7Bn%7D%7D%3D%5C%20%5C%20Kaava%5C%20MAOL%3Assa!" alt="s=\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=\ \ Kaava\ MAOL:ssa!"/><br/>
<img src="https://math-demo.abitti.fi/math.svg?latex=s%3D%5Csqrt%7B%5Cfrac%7B0%7B%2C%7D08609271523178807947%5Ccdot(1-0%7B%2C%7D08609271523178807947)%7D%7B302%7D%7D" alt="s=\sqrt{\frac{0{,}08609271523178807947\cdot(1-0{,}08609271523178807947)}{302}}"/>= 0,0161410....<br/>
<br/>
<p>Lasku laitettu speedcrunchiin:<br/>
sqrt(0{,}08609271523178807947*(1-0{,}08609271523178807947)/302)</p>
<p>= 0,0161410134938494557</p>
<p><img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%5B0%7B%2C%7D08609271523178807947-1%7B%2C%7D96s%5C%20%3B%5C%200%7B%2C%7D08609271523178807947%2B1%7B%2C%7D96s%5Cright%5D" alt="\left[0{,}08609271523178807947-1{,}96s\ ;\ 0{,}08609271523178807947+1{,}96s\right]"/>=<br/>
[0,05436... ; 0,1176...] <br/>
<img src="https://math-demo.abitti.fi/math.svg?latex=%5Capprox%5Cleft%5B0%7B%2C%7D054%5C%20%3B%5C%200%7B%2C%7D12%5C%20%5Cright%5D" alt="\approx\left[0{,}054\ ;\ 0{,}12\ \right]"/></p>
<p>V: Luottamusväli noin <img src="https://math-demo.abitti.fi/math.svg?latex=%5Capprox%5Cleft%5B0%7B%2C%7D054%5C%20%3B%5C%200%7B%2C%7D12%5C%20%5Cright%5D" alt="\approx\left[0{,}054\ ;\ 0{,}12\ \right]"/><br/>
<br/>
<br/>
<a href="https://peda.net/p/leena.k./mab-8/4tp/4l/er/4062/868a2413-7177-4d07-9fd3-dbd7941abbd0.png#top" title="868A2413-7177-4D07-9FD3-DBD7941ABBD0.png"><img src="https://peda.net/p/leena.k./mab-8/4tp/4l/er/4062/868a2413-7177-4d07-9fd3-dbd7941abbd0.png:file/photo/ac20af4c1fed222cf6ea57c6c4a1fb590356d47a/868A2413-7177-4D07-9FD3-DBD7941ABBD0.png" alt="" title="868A2413-7177-4D07-9FD3-DBD7941ABBD0.png" class="inline" loading="lazy"/></a><br/>
<br/>
</p>
2021-11-09T10:34:11+02:00
408
https://peda.net/id/d4c170da5e7
2022-11-07T11:09:11+02:00
<a href="https://peda.net/p/leena.k./mab-8/4tp/4l/er/408/408.jpg#top" title="408.jpg"><img src="https://peda.net/p/leena.k./mab-8/4tp/4l/er/408/408.jpg:file/photo/e9df2e933776028c6cbed4f6288c0999c8a2b872/408.jpg" alt="" title="408.jpg" class="inline" loading="lazy"/></a>
2022-11-07T11:09:06+02:00
411.
https://peda.net/id/e74f27ae413
2021-11-09T10:07:42+02:00
[[$ \left[ \bar{x}-3,29\dfrac{s}{\sqrt{n}};\ \bar{x}+3,29\dfrac{s}{\sqrt{n}} \right] $]] <strong class="editor red">tehtävässä ei ole kerrottu keskihajontaa tai otoksen kokoa, joten ei onnistu tällä tavoin.</strong><br/>
<br/>
<p>Otoksen keskiarvo on luottamusvälin rajojen keskiarvo, joten otoksen keskiarvo on<span class="small"><a href="https://peda.net/p/leena.k./mab-8/4tp/4l/er/411/411.jpg#top" title="411.jpg"><img src="https://peda.net/p/leena.k./mab-8/4tp/4l/er/411/411.jpg:file/photo/a61ece0f469d64bb6b3255da3acaa32e910efe4c/411.jpg" alt="" title="411.jpg" class="inline" loading="lazy"/></a></span><br/>
<br/>
<img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7B10%7B%2C%7D1%2B14%7B%2C%7D3%7D%7B2%7D%3D12%7B%2C%7D2" alt="\frac{10{,}1+14{,}3}{2}=12{,}2"/><br/>
<br/>
</p>
<p>(Lasku speedcrunchilla:(10,1+14,3)/2</p>
<p>= 12,2)<br/>
<br/>
V: <img src="https://math-demo.abitti.fi/math.svg?latex=%5Coverline%7Bx%7D%3D12%7B%2C%7D2" alt="\overline{x}=12{,}2"/></p>
<p><span> </span></p>
<p> </p>
2021-11-09T09:59:02+02:00
412.
https://peda.net/id/b32226f4413
2021-11-09T14:48:11+02:00
a) n=100<br/>
<img src="https://math-demo.abitti.fi/math.svg?latex=%5Coverline%7Bx%7D%3D66%5C%20mm" alt="\overline{x}=66\ mm"/><br/>
<img src="https://math-demo.abitti.fi/math.svg?latex=s%3D1%5C%20mm" alt="s=1\ mm"/><br/>
<br/>
<p>Muuttujana on n=100 kappaleen otosten keskiarvo. <strong class="editor red">Keskiarvon keskihajonta saadaan keskiarvon keskivirheen kaavalla</strong> (kuinka paljon kesmäärin poikkeaa keskiarvosta). Perusjoukon keskihajonta on s=1 mm, joten <br/>
<br/>
<br/>
<img src="https://math-demo.abitti.fi/math.svg?latex=s_%7B%5Coverline%7Bx%7D%7D%3D%5Cfrac%7Bs%7D%7B%5Csqrt%7Bn%7D%7D" alt="s_{\overline{x}}=\frac{s}{\sqrt{n}}"/><br/>
<img src="https://math-demo.abitti.fi/math.svg?latex=s_%7B%5Coverline%7Bx%7D%7D%3D%5Cfrac%7B1mm%7D%7B%5Csqrt%7B100%7D%7D%3D0%7B%2C%7D1%5C%20mm" alt="s_{\overline{x}}=\frac{1mm}{\sqrt{100}}=0{,}1\ mm"/><br/>
<br/>
<img src="https://math-demo.abitti.fi/math.svg?latex=V%3A%5C%200%7B%2C%7D1%5C%20mm" alt="V:\ 0{,}1\ mm"/></p>
<p> </p>
<p>b) <br/>
<img src="https://math-demo.abitti.fi/math.svg?latex=s_%7B%5Coverline%7Bx%7D%7D%3D%5Cfrac%7Bs%7D%7B%5Csqrt%7Bn%7D%7D" alt="s_{\overline{x}}=\frac{s}{\sqrt{n}}"/><br/>
<img src="https://math-demo.abitti.fi/math.svg?latex=n%3D625" alt="n=625"/><br/>
<img src="https://math-demo.abitti.fi/math.svg?latex=s_%7B%5Coverline%7Bx%7D%7D%3D0%7B%2C%7D04%5C%20mm" alt="s_{\overline{x}}=0{,}04\ mm"/></p>
<div><br/>
<img src="https://math-demo.abitti.fi/math.svg?latex=0%7B%2C%7D04%5C%20mm%3D%5Cfrac%7Bs%7D%7B%5Csqrt%7B625%7D%7D" alt="0{,}04\ mm=\frac{s}{\sqrt{625}}"/><br/>
<img src="https://math-demo.abitti.fi/math.svg?latex=s%3D0%7B%2C%7D04%5C%20mm%5Ccdot%5Csqrt%7B625%7D" alt="s=0{,}04\ mm\cdot\sqrt{625}"/></div>
<p><br/>
<img src="https://math-demo.abitti.fi/math.svg?latex=s%3D1%5C%20mm" alt="s=1\ mm"/></p>
<div>Speedcrunchilla laskettuna:</div>
<div> 0,04*sqrt(625)<br/>
= 1</div>
<div><br/>
<div><img src="https://math-demo.abitti.fi/math.svg?latex=V%3A%5C%201%5C%20mm" alt="V:\ 1\ mm"/></div>
</div>
2021-11-09T10:19:03+02:00
414
https://peda.net/id/2ad4d88a5e7
2022-11-07T11:20:22+02:00
<br/>
<strong class="editor red">koska n=12<30 joudut laskemaan keskiarvon keskivirheen <img src="https://math-demo.abitti.fi/math.svg?latex=s_%7B%5Coverline%7Bx%7D%7D" alt="s_{\overline{x}}"/></strong><br/>
<a href="https://peda.net/p/leena.k./mab-8/4tp/4l/er/414/414a.jpg#top" title="414a.jpg"><img src="https://peda.net/p/leena.k./mab-8/4tp/4l/er/414/414a.jpg:file/photo/0f3a65e65a790a54078c112b4b33ba0385d9cff2/414a.jpg" alt="" title="414a.jpg" class="inline" loading="lazy"/></a>
2022-11-07T11:18:40+02:00
415
https://peda.net/id/33be965e5f6
2022-11-08T14:35:22+02:00
<br/>
<br/>
<a href="https://peda.net/p/leena.k./mab-8/4tp/4l/er/415/415a.jpg#top" title="415a.jpg"><img src="https://peda.net/p/leena.k./mab-8/4tp/4l/er/415/415a.jpg:file/photo/2ae1770a1e1064b2c2e00ef62df89ff3c4390709/415a.jpg" alt="" title="415a.jpg" class="inline" loading="lazy"/></a><br/>
<a href="https://peda.net/p/leena.k./mab-8/4tp/4l/er/415/415b.jpg#top" title="415b.jpg"><img src="https://peda.net/p/leena.k./mab-8/4tp/4l/er/415/415b.jpg:file/photo/7eec1b2df2a6a78564717f3bf7b19bfd25181667/415b.jpg" alt="" title="415b.jpg" class="inline" loading="lazy"/></a><br/>
<br/>
<a href="https://peda.net/p/leena.k./mab-8/4tp/4l/er/415/415-c.jpg#top" title="415 c.jpg"><img src="https://peda.net/p/leena.k./mab-8/4tp/4l/er/415/415-c.jpg:file/photo/f03a6d5a97f68fe777fdacc091c45ae2ee44c6ee/415%20c.jpg" alt="" title="415 c.jpg" class="inline" loading="lazy"/></a>
2022-11-08T14:31:00+02:00