【高校数学B】2-2-2 正規分布｜問題集
1.次の正規分布表を見て答えなさい。
| \(z_0\) | \(.00\) | \(.03\) | \(.05\) | \(.06\) | \(.07\) | \(.08\) |
| \(0.2\) | \(\tiny 0.0793\) | \(\tiny 0.0910\) | \(\tiny 0.0987\) | \(\tiny 0.1026\) | \(\tiny 0.1064\) | \(\tiny 0.1103\) |
| \(0.5\) | \(\tiny 0.1915\) | \(\tiny 0.2109\) | \(\tiny 0.2088\) | \(\tiny 0.2123\) | \(\tiny 0.2157\) | \(\tiny 0.2190\) |
| \(0.8\) | \(\tiny 0.2881\) | \(\tiny 0.2967\) | \(\tiny 0.3023\) | \(\tiny 0.3051\) | \(\tiny 0.3078\) | \(\tiny 0.3106\) |
| \(1.0\) | \(\tiny 0.3413\) | \(\tiny 0.3485\) | \(\tiny 0.3531\) | \(\tiny 0.3554\) | \(\tiny 0.3577\) | \(\tiny 0.3599\) |
| \(1.2\) | \(\tiny 0.3849\) | \(\tiny 0.3907\) | \(\tiny 0.3944\) | \(\tiny 0.3962\) | \(\tiny 0.3980\) | \(\tiny 0.3997\) |
| \(1.6\) | \(\tiny 0.4452\) | \(\tiny 0.4484\) | \(\tiny 0.4505\) | \(\tiny 0.4515\) | \(\tiny 0.4525\) | \(\tiny 0.4535\) |
| \(1.9\) | \(\tiny 0.4713\) | \(\tiny 0.4732\) | \(\tiny 0.4744\) | \(\tiny 0.4750\) | \(\tiny 0.4756\) | \(\tiny 0.4761\) |
| \(2.0\) | \(\tiny 0.4772\) | \(\tiny 0.4788\) | \(\tiny 0.4798\) | \(\tiny 0.4803\) | \(\tiny 0.4808\) | \(\tiny 0.4812\) |
| \(2.3\) | \(\tiny 0.4893\) | \(\tiny 0.4901\) | \(\tiny 0.4906\) | \(\tiny 0.4909\) | \(\tiny 0.4911\) | \(\tiny 0.4913\) |
| \(2.5\) | \(\tiny 0.4938\) | \(\tiny 0.4943\) | \(\tiny 0.4946\) | \(\tiny 0.4948\) | \(\tiny 0.4949\) | \(\tiny 0.4951\) |
(1)確率変数\(Z\)が標準正規分布\(N(0,1)\)に従うとき、次の確率を求めなさい。
①\(P(-1\leqq Z\leqq 1)\)
②\(P(Z\geqq -0.5)\)
(2)確率変数\(X\)が正規分布\(N(1,4^2)\)に従うとき、\(P(2\leqq X\leqq 9)\)を求めなさい。
(3)昆虫\(100\)匹の体長平均が\(19.6\)mm、標準偏差が\(0.5\)mmのとき、\(20\)mm以上はおよそ何匹か求めなさい。
2.成功率が\(96\)%である。これを\(150\)回試行したとき、成功が\(140\)回以下になる確率を求めなさい。
次の学習に進もう！