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TABLE 1.10.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.090.50.00.504 0.508 0.5120.516 0.5199 0.52390.5279 0.53190.5359 0.0753 0.1985596 0.5636 0.56750.5793 0.5832 05871 0.591 0.59480.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.648 0.6517 0.3879 0.40.40.50.60.6554 0.6591 0.6628 0.6664 0.67 0.6736 0.6772 0.6808 0.68446985 0.7019 0.7054 0.7088 0.716915 0.6950.230.7157 0.7197549 0.6611 0.7642 0.7673 0.7704 0.7734 0.770.7881| 0791-TO79390.8365 0.8389 0.90.91.08186 0.8212 0.8238 0.8264 0.8289 0.8315 0.83400.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.86215 0.8686 0.8708 0.8729 0.8749 0.877 0.879 0.881 0.883 1.169 0.8888 0.8907 0.8925 0.8944 0.8962 0.898 0.89979049 0.9066 0.90820.90320.9177 1.393450.9357 0.937 0.93829418 0.9429441 11.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545 1.60.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.70.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 1.81.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.975 0.9756 0.9761 0.9767 1.9817 2.02.110.9884 0.9887 0.989 2.22.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.979834 0.9838 0.9842 0.9846 0.985 0.9854 0.98570.9821 0.9826 0.983 0.98342.20.9868 0.98710.9898 O875 0.98780.9931 0.9932 0.9934 0.9936 240.9938 0.994 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 2.50.9956 0.9957 0.9959 0.996 0.9961 0.9962 0.9963 0.9964 2.60.9918 0.992 0.9922 0.9925 0.9927 0.99292.52.6 0.9953 0.9955622.7 0.9965 0.99660.9967 0.9968 0.9969 0.997 0.9971 0.99720.9973 0.9974 2.7977 0.99782.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986 2.93.00.9988 0.9988 0.9989 0.9989 0.9989 0.999 0.9990.999 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992.9992 0.9993 0.9993 3.13.2 0.9993 0.99930.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 3.23.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.999 0.9996 0.9997 3.33.3.3.64 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998 3.45 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 3.50.9998 0.9998 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 3.63.83.98 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 3.80.00 0.01 0.020.03 0.04 0.05 0.06 0.07 0.08 0.09 Z

Question

Refer to the attached photo for the table. 

 

  1. What is the probability of a z-score greater than -1.97?
TABLE 1.1
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.5
0.0
0.504 0.508 0.5120.516 0.5199 0.5239
0.5279 0.5319
0.5359 0.0
753 0.1
98
5596 0.5636 0.5675
0.5793 0.5832 05871 0.591 0.5948
0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.648 0.6517 0.3
879 0.4
0.4
0.5
0.6
0.6554 0.6591 0.6628 0.6664 0.67 0.6736 0.6772 0.6808 0.6844
6985 0.7019 0.7054 0.7088 0.71
6915 0.6950.
23
0.7157 0.719
7549 0.6
611 0.7642 0.7673 0.7704 0.7734 0.77
0.7881| 0791-TO7939
0
.8365 0.8389 0.9
0.9
1.0
8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340
0.
8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621
5 0.8686 0.8708 0.8729 0.8749 0.877 0.879 0.881 0.883 1.1
69 0.8888 0.8907 0.8925 0.8944 0.8962 0.898 0.8997
9049 0.9066 0.9082
0.9032
0.91
77 1.3
9345
0.9357 0.937 0.9382
9418 0.942
9441 1
1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545 1.6
0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.7
0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 1.8
1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.975 0.9756 0.9761 0.9767 1.9
817 2.0
2.1
10.9884 0.9887 0.989 2.2
2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798
34 0.9838 0.9842 0.9846 0.985 0.9854 0.9857
0.9821 0.9826 0.983 0.9834
2.2
0.9868 0.9871
0.9898 O
875 0.9878
0.9931 0.9932 0.9934 0.9936 24
0.9938 0.994 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 2.5
0.9956 0.9957 0.9959 0.996 0.9961 0.9962 0.9963 0.9964 2.6
0.9918 0.992 0.9922 0.9925 0.9927 0.9929
2.5
2.
6 0.9953 0.9955
62
2.7 0.9965 0.99660.9967 0.9968 0.9969 0.997 0.9971 0.99720.9973 0.9974 2.7
977 0.9978
2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986 2.9
3.0
0.9988 0.9988 0.9989 0.9989 0.9989 0.999 0.999
0.999 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992.9992 0.9993 0.9993 3.1
3.2 0.9993 0.99930.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 3.2
3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.999 0.9996 0.9997 3.3
3.
3.
3.6
4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998 3.4
5 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 3.5
0.9998 0.9998 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 3.6
3.8
3.9
8 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 3.8
0.00 0.01 0.020.03 0.04 0.05 0.06 0.07 0.08 0.09 Z
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TABLE 1.1 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.5 0.0 0.504 0.508 0.5120.516 0.5199 0.5239 0.5279 0.5319 0.5359 0.0 753 0.1 98 5596 0.5636 0.5675 0.5793 0.5832 05871 0.591 0.5948 0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.648 0.6517 0.3 879 0.4 0.4 0.5 0.6 0.6554 0.6591 0.6628 0.6664 0.67 0.6736 0.6772 0.6808 0.6844 6985 0.7019 0.7054 0.7088 0.71 6915 0.6950. 23 0.7157 0.719 7549 0.6 611 0.7642 0.7673 0.7704 0.7734 0.77 0.7881| 0791-TO7939 0 .8365 0.8389 0.9 0.9 1.0 8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0. 8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621 5 0.8686 0.8708 0.8729 0.8749 0.877 0.879 0.881 0.883 1.1 69 0.8888 0.8907 0.8925 0.8944 0.8962 0.898 0.8997 9049 0.9066 0.9082 0.9032 0.91 77 1.3 9345 0.9357 0.937 0.9382 9418 0.942 9441 1 1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545 1.6 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.7 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 1.8 1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.975 0.9756 0.9761 0.9767 1.9 817 2.0 2.1 10.9884 0.9887 0.989 2.2 2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 34 0.9838 0.9842 0.9846 0.985 0.9854 0.9857 0.9821 0.9826 0.983 0.9834 2.2 0.9868 0.9871 0.9898 O 875 0.9878 0.9931 0.9932 0.9934 0.9936 24 0.9938 0.994 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 2.5 0.9956 0.9957 0.9959 0.996 0.9961 0.9962 0.9963 0.9964 2.6 0.9918 0.992 0.9922 0.9925 0.9927 0.9929 2.5 2. 6 0.9953 0.9955 62 2.7 0.9965 0.99660.9967 0.9968 0.9969 0.997 0.9971 0.99720.9973 0.9974 2.7 977 0.9978 2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986 2.9 3.0 0.9988 0.9988 0.9989 0.9989 0.9989 0.999 0.999 0.999 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992.9992 0.9993 0.9993 3.1 3.2 0.9993 0.99930.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 3.2 3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.999 0.9996 0.9997 3.3 3. 3. 3.6 4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998 3.4 5 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 3.5 0.9998 0.9998 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 3.6 3.8 3.9 8 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 3.8 0.00 0.01 0.020.03 0.04 0.05 0.06 0.07 0.08 0.09 Z

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Step 1

The normal distribution:

A continuous random variable X is said to follow normal distribution if the probability density function of X is,

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Step 2

The z-score:

The ­z-score corresponding to the value x of a normally distributed variable, X with mean  and standard deviation  can be obtained as:

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Step 3

An important property of the normal distribution:

The normal distribution is symmetric. Thus, for any pai...

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