Question

Copy of If Z is a standard normal random variable, find P(-1.7 <Z < 2.6). 0.4217 0.9507 -0.9508 0.9953 0.0446

Answer 1

OPTION "B" 0.9507 IS CORRECT

TO OBTAIN THE ANSWER WE NEED TO FOLLOW SEVERAL STEPS THAT ARE GIVEN BELOW

Step 1: Sketch the curve. The probability that -1.7<7<2.6 is equal to the blue area under the curve. 0.50 0.45 0.40 0.35 0.30 0.25 у 0.20 0.15 0.10- 0.05 0.00 -1.7 2.6 -0.05 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 .5 2.0 2.5 3.0 3.5 X Step 2: To find the probability of P(-1.7<7<2.6), we use the following formula: P(-1.7<2<2.6)=P(Z <2.6) - P(Z <-1.7) Step 3: P(Z <2.6 ) can be found by using the following standard normal table.

0.09 Z 0.0 0.1 02 03 04 05 06 0.7 08 09 1.0 11 12 13 14 1.5 16 17 1.8 19 20 21 0.00 0.01 0.02 0.03 0.04 10.05 0.06 0.07 0.08 0.5 0.504 0.508 0512 0.516 0.5199 0.5239 0.5279 0.5319 0.5359 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.5793 0.5832 0.5871 0.591 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141 06179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.648 0.6517 0.6554 0.6591 0.6628 0.6664 067 0.67 36 0.5772 0.6808 0.6844 0.6879 0.6915 0.695 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0719 0.7224 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.758 07611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 07881 0791 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 08159 0.818 0.82 12 0.8238 0.826/ 0.8289 0.8315 0.834 0.8365 0.83 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.857 0.8599 0.8621 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.877 0.879 0.881 0.883 0.849 0.8869 0.888 0.8907 0.8925 0.8944 0.8962 0.898 0.8997 0.90 15 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 0.9332 0.9345 0.9357 0.937 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.96 16 0.9625 0.9633 09641 0.9649 0.9656 0.9664 0.9571 0.9578 0.9686 0.9593 0.9599 0.9706 0.9713 0.97 19 0.9726 09732 0.9738 0.9744 0.975 0.9756 0.9761 0.9767 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817 09821 0.9826 0983 0.9834 0.9838 0.9842 0.9846 0985 0.9854 0.9857 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.989 0.9893 0.986 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916 0.9918 0.992 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936 0.993 0.994 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 0.9953 0.9955 0.9956 0.9957 09959 0.996 0.9961 0.9962 0.9963 0.9964 0.9965 0.9966 0.9967 0.9968 0.9969 0.997 0.9971 0.9972 0.9973 0.9974 22 2.3 24 2.5 2.6 27

We see that P(Z < 2.6 ) = 0.9953. Step 4: P(Z < -1.7 ) can be found by using the following fomula. P(Z <-a)=1 - P(Z <a) After substituting a = 1.7 we have: P(Z < -1.7) = 1- P(Z <1.7) P(Z < 1.7 ) can be found by using the following standard normal table.

Z Z 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 23 2.4 2.5 2.6 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.5 0.504 0.508 0.512 0.516 0.5199 0.5239 0.5279 0.5319 0.5359 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.5793 0.5832 0.5871 0.591 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.648 0.6517 0.6554 0.6591 0.6628 0.6664 0.67 0.6736 0.6772 0.6808 0.6844 0.6879 0.6915 0.695 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.719 0.7224 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.758 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 0.7881 0.791 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.834 0.8365 0.8389 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.877 0.879 0.881 0.883 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.898 0.8997 0.9015 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 0.9332 0.9345 0.9357 0.937 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.975 0.9756 0.9761 0.9767 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817 0.9821 0.9826 0.983 0.9834 0.9838 0.9842 0.9846 0.985 0.9854 0.9857 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.989 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916 0.9918 0.992 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936 0.9938 0.994 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 0.9953 0.9955 0.9956 0.9957 0.9959 0.996 0.9961 0.9962 0.9963 0.9964

We see that P ( 2<1.7) = 0.9554 so, P(Z < -1.7) = 1 - P(Z <1.7)=1 -0.9554 = 0.0446 At the end we have: P(-1.7<7 < 2.6 ) = 0.9507

IN THIS WAY WE FIND THE VALUE OF P(-1.7<Z<2.6) = 0.9507

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