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Mathematics Undergraduate

5つ問題があります。わかる方お願いします

16:48 8 課題 以下の内容を読み進めて、5つの問題に答えてください。 計算の際は、電卓やRを使っていただいて構いません。 ある選挙において, 候補者は二人(AさんとBさんとします) で, 投票者の全員がどちらかに投票しているとします。 話 を聞いた人をn, そのうちAさんに投票する人をk, Aさんの得票率をRとすると以下のような確率モデルが書けます。 \[ P(X=k) = {_nC_k R^k(1-R)^{n-k} \] 1. ここから 得票率Rが50%の時, 10人に話を聞いて (n=10), A投票する人が0人 (k=0) という場合が起こる確率を求 めてください。 2.Rとnは同じでAに投票する人が10人の時の確率を求めてください。 3.Rとnは同じでAに投票する人が5人の時の確率を求めてください。 上記の確率分布は二項分布と呼ばれ、平均 \(np\), 分散 \ (np (1-p)\) です。 中心極限定理からnが十分に大きい時、 正規 分布に従うことがわかっています。 正規分布は以下のように範囲ごとに確率が決まっていま す。 ・標準偏差(\(\sigma\)), 平均 (\(\mu\)) ■1シグマ範囲 \(\mu\sigma \le X \le \mu + \sigma\) 確率68.3% ■2シグマ範囲 \(\mu-2\sigma \le X \le \mu + 2\sigma\) 確率95.4% ■3シグマ範囲 \(\mu-3\sigma \le X \le \mu + 3\sigma\) 確率99.7% • \(\mu - 1.96\sigma \le X \le \mu +1.96\sigma\) の 範囲が確率95%です a 三 [24] 8・ 9 これを使うと、真の得票率Rは95%の確率で \[r-1.96 \sqrt(\frac{r(1-r)}{n}} \le R \ler + 1,96\sqrt{\frac{r(1-r)}{n}} \] に含まれると計算できます (詳しい計算は省略します)。 4.今,500人に出口調査をして、 Aの得票率が58%だったとします。 この時、真の得票率Rはどんな範囲に入ります か? 5. この計算結果から、 選挙の結果について言えることはなんですか?

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TOEIC・English Undergraduate

自分の回答と照らし合わせて確認したいので、答えがなにになるかどなたか教えてください。 解説もあると助かります。

5 A Matter of Taste Reading Passage 042 At the age of just 22, Jamie Oliver became well known across the UK as "The Naked Chef." He called himself this not because he cooked wearing no clothes, but because he wanted to simplify food preparation so that everybody could follow his recipes. He wanted to "strip down" the idea of cooking. Since then he has had numerous TV shows, published 50 many books, and has become a household name in the UK. Today, one of the activities Jamie Oliver is best known for is his great effort to improve the school dinners that children eat every day. One day, he visited the kitchen of a typical London secondary school, and he was shocked to see how much processed junk food the kids were given to eat each day. Fat and sugar levels were extremely high, and nutritional values very 10 low. The "turkey twizzler" became the symbol of these unhealthy meals: processed meat containing 21.2% fat and only 34% actual turkey. Oliver ran the school kitchen for one year and tried to show that it was possible to serve healthy meals on a limited budget—and that kids actually enjoyed eating them. His mission was to radically change the eating habits of children in that school, and across the country. 150 200 15 20 25 CULTIES 250 His project (the "Feed Me Better" campaign) has had some influence on school dinners in the UK. After watching the documentary Jamie's School Dinners, 271,677 people signed a petition calling for healthier school meals. This led the Prime Minister to agree to spend 280 million pounds (about 37 billion yen) on school dinners, to ban some junk food from school menus, and to create a School Food Trust to provide support and advice for people preparing school meals. Research, by the way, shows that children who stop eating sugary, fatty food and instead eat Oliver's school dinners are better behaved in class, and they get higher test 300 scores, too. 350 Of course, the project has had some problems. At first, many students (and even parents) resisted the removal of the junk food they were so used to. In one famous instance, some parents were passing local takeaway food to their children through the school fence. Also, schools that followed the plan for a while were often found to gradually drift back into bad habits. After all, it is easier and cheaper to just give the kids junk food. However, Oliver's efforts represent a positive start, and with obesity becoming such a huge problem (see Unit 4), 400 it's a very necessary start.

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