题目
若随机变量Z~N(0,1),查标准正态分布表,求:(1)P(Z≤2.75);(2)P(Z<0.5);(3)P(Z>-1.5);(4)P(2<Z<2.9);(5)P(-2<Z≤2.9).x o 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09-|||-0 0.5000 0.5040 0.5080 0.5120 0.5160 0.519 9 0.523 9 0.527 9 0.5319 0.535 9-|||-0.1 0.5398 0.543 8 0.5478 0.551 7 0.555 7 0.559 6 0.5636 0.567 5 0.5714 0.575 3-|||-0.2 579 3 0.5832 0.5871 0.591 0 0.594 8 0.598 7 0.6026 0.606 4 0.610 3 0.614 1-|||-0.3 0.617 9 0.621 7 0.625 5 0.629 3 0.633 1 0.636 8 0.640 4 0.644 3 0.6480 0.651 7-|||-0.4 0.6554 0.659 1 0.6628 0.666 4 0.670 0 0.673 6 0.6772 0.680 8 0.684 4 0.687 9-|||-0.5 0.691 5 0.6950 0.698 5 0.701 9 0.705 4 0.708 8 0.7123 0.715 7 0.7190 0.7224-|||-0.6 0.725 7 0.729 1 0.7324 0.735 7 0.738 9 0.7422 0.7454 0.748 6 0.7517 0.754 9-|||-0.7 0.7580 0.761 1 0.764 2 0.7673 0.770 3 0.773 4 0.776 4 0.779 4 0.782 3 0.785 2-|||-0.8 0.788 1 0.791 0 0.793 9 0.796 7 0.799 5 0.802 3 0.805 1 0.807 8 0.810 6 0.813 3-|||-0.9 0.815 9 0.818 6 0.821 2 0.823 8 0.8264 0.828 9 0.8355 0.8340 0.836 5 0.838 9-|||-1 0.841 3 0.843 8 0.8461 0.848 5 0.850 8 0.853 1 0.8554 0.857 7 0.859 9 0.862 1-|||-1.1 0.864 3 0.866 5 0.868 6 0.870 8 0.872 9 0.874 9 0.877 0 0.8790 0.881 0 0.883 0-|||-1.2 0.884 9 0.886 9 0.888 8 0.890 7 0.892 5 0.894 4 0.8962 0.898 0 0.899 7 0.901 5-|||-1.3 0.903 2 0.904 9 0.906 6 0.908 2 0.909 9 0.911 5 0.913 1 0.914 7 0.916 2 0.917 7-|||-1.4 0.919 2 0.920 7 0.922 2 0.923 6 0.925 1 0.926 5 0.927 9 0.929 2 0.9306 0.9319-|||-1.5 0.9332 0.934 5 0.935 7 0.9370 0.938 2 0.9394 0.940 6 0.941 8 0.943 0 0.944 1-|||-1.6 0.9452 0.946 3 0.9474 0.948 4 0.949 5 0.950 5 0.951 5 0.952 5 0.953 5 0.953 5-|||-1.7 0.955 4 0.956 4 0.9573 0.958 2 0.959 1 0.959 9 0.9608 0.961 6 0.962 5 0.963 3-|||-8 0.964 1 0.9648 0.9656 0.966 4 0.9672 0.9678 0.968 6 0.969 3 0.9700 0.970 6-|||-1.9 0.971 3 0.9719 0.972 6 0.973 2 0.973 8 0.974 4 0.9750 0.975 6 0.9762 0.976 7-|||-2 0.977 2 0.977 8 0.978 3 0.978 8 0.979 3 0.979 8 0.9803 0.980 8 0.981 2 0.981 7-|||-2.1 0.982 1 0.9826 0.9830 0.983 4 0.983 8 0.984 2 0.9846 0.9850 0.985 4 0.985 7-|||-2.2 0.986 1 0.986 4 0.986 8 0.9871 0.9874 0.9878 0.988 1 0.988 4 0.988 7 0.9890-|||-2.3 0.989 3 0.9896 0.989 8 0.990 1 0.9904 0.9906 0.9909 0.991 1 0.991 3 0.991 6-|||-2.4 0.991 8 0.9920 0.9922 0.992 5 0.992 7 0.9929 0.993 1 0.993 2 0.993 4 0.993 6-|||-2.5 0.993 8 0.9940 0.994 1 0.994 3 0.994 5 0.9946 0.9948 0.994 9 0.995 1 0.995 2-|||-2.6 0.9953 0.995 5 0.995 6 0.995 7 0.9959 0.9960 0.996 1 0.996 2 0.996 3 0.996 4-|||-2.7 0.996 5 0.996 6 0.996 7 0.996 8 0.996 9 0.9970 0.9971 0.9972 0.9973 0.9974-|||-2.8 0.9974 0.9975 0.9976 0.997 7 0.997 7 0.9978 0.9979 0.997 9 0.998 0 0.998 1-|||-9 0.998 1 0.998 2 0.998 2 0.998 3 0.998 4 0.998 4 0.998 5 0.998 5 0.998 6 0.998 6
若随机变量Z~N(0,1),查标准正态分布表,求:
(1)P(Z≤2.75);
(2)P(Z<0.5);
(3)P(Z>-1.5);
(4)P(2<Z<2.9);
(5)P(-2<Z≤2.9).

(1)P(Z≤2.75);
(2)P(Z<0.5);
(3)P(Z>-1.5);
(4)P(2<Z<2.9);
(5)P(-2<Z≤2.9).

题目解答
答案
解:(1)P(Z≤2.75)=0.9970;
(2)P(Z<0.5)=0.6915;
(3)P(Z>-1.5)=P(Z<1.5)=0.9332;
(4)P(2<Z<2.9)=P(Z<2.9)-P(Z≤2)=0.9981-0.9772=0.0209;
(5)P(-2<Z≤2.9)=P(Z≤2.9)-P(Z≤-2)=P(Z≤2.9)-[1-P(Z<2)]=0.9881-(1-0.9772)=0.9753.
(2)P(Z<0.5)=0.6915;
(3)P(Z>-1.5)=P(Z<1.5)=0.9332;
(4)P(2<Z<2.9)=P(Z<2.9)-P(Z≤2)=0.9981-0.9772=0.0209;
(5)P(-2<Z≤2.9)=P(Z≤2.9)-P(Z≤-2)=P(Z≤2.9)-[1-P(Z<2)]=0.9881-(1-0.9772)=0.9753.