Question
I'm having trouble getting the correct calculations. I will attach the problem which has 5 parts as well as the required data to solve this.
my answers:
part A, I got x=40.06
z=-0.5
using the cumulative standard normal distribution table I got p(z<40.06)=0.3089
part B, I got x=40.82
z=+0.5
using the same table I got p(z>40.82)=0.6195
* this has to be wrong because shouldn't it equal 0.3089 like the other one?
part C, I couldn't calculate
part d, I got extremely off numbers 25th percentile was 5.0cm. 75th percentile was 15.0 cm.
*this is also wrong.
part e, I got critical=39.677 cm
z=-1.0
after looking at the table I got p(x<39.677)=0.1587
*the probability might be wrong.
please show work
SECTION C.3: Cumulative Standard Normal Distribution 0.00 0.01 0.02 0.03 0,04 0.06 0.06 0 -0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.17110,1685 0.1660 -0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 1 -0.7 0.2420 0.2389 0.2358 0.2327 0.2206 0.22660.2236 0.2206 -0.6 0.2743 0.2709 0.2676 0.2613 0.2611 0.2578 02546 02510 0.2453o 0.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 0.28 -0.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3669 0.3632 0.3594 0.3557 0.3520 0.3483 -0.3 0.3821 0.3783 0.3745 0.3707 -0.2 0.4207 0.4168 0.4129 0.4090 0.4052 0.4013 0.397 -0.1 0.4602 0:4562 0.4522 0.4483 0.4443 0 -0.0 0.5000 0.4960 0.4920 0.4880 0.4404 0.4364 0.4325 0.4286 0.4247 0.4840 0.4801 0.4761 0.4721 0.4681 0.4641 0.5596 0.5636 0.5675 0.5714 0.5753 0.6368 0.6406 0.6443 0.6480 0.6517 0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279531o 0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.4 0.6534 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.7 0.758o 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.T852 0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 08078 0.8106 0.8133 0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 0.68080.68440.6879 1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621 1.1 0.S643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8820 1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 o.so15 1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.97500.9756 0.9761 0.9767 2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817 2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890 2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916 2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936 2.5 0.9938 0.9940 0.99410.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9 2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964 2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981 2.9 0.9981 0.9982 0.9982 0.9983 09984 0.9984 0.9985 0.9985 0.9986 0.998 3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990 3.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.993 3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997 3.4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998 3.5 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 3.6 0.9998 0.9998 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 3.7 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 3.8 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 09999 3.9 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
Explanation / Answer
I will correct your answer.
In part A P(Z<-0.5) =0.3085 is your answer is correct.
In part B P(Z>0.5) = 1-P(Z<0.5) ===>> Normal distribution gives always < probabilty.
=1-0.6915
=0.3085 which is same like other.
Part C: It is very easy.
P(-0.5<Z<0.5) = P(Z<0.5)-P(<-0.5)
=0.6915-0.3085=0.3830
Hope this will be helpful. Thanks and God Bless You :)
