Question

QUESTION 19 Sale SHS, wyremally distried with a 80 and standard deviation and the mean and standard deviation of students final scores in Statistical we do not know the exact distribution of Y Assume that you are selecting only one student from the Statistical Methods I class, and 49 students from the Step at the final score of the selected adent from Statistical Methods I class is higher than a certain score (say") is 09542. Find the value of

Answer 1

We have to deal with score at Statistical Methods I :

Here X ~ N($\small \mu$ = 80, =8)

0

Note that,

$\small Let \ Z=\frac{X-\mu}{\sigma}\sim N(0,1)$

$\small P(Z\le z)=\Phi(z) \ and \ \Phi(-z)=1-\Phi(z)$

Given that,

PX > k) = 0.9842

$or, \ 1-P(\frac{X-\mu}{\sigma}\le \frac{k-80}{8})=0.9842$

$or, \ \Phi(\frac{k-80}{8})=0.0158=\Phi(-2.15)$       (Value from z table)

$or, \ \frac{k-80}{8}=-2.15$

Therefore, the value of k is 62.8.

z table :

Z 0.0 0.1 02 03 0.4 05 0.6 0.7 0.8 0.9 1.0 1.1 12 13 14 15 1.6 17 18 1.9 2.0 21 22 23 2.4 25 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 0.00 0.5000 05398 0.5793 0.6179 0.6554 0.6915 0.7257 0.7580 0.7881 0.8159 0.8413 0.8643 0.8849 0.9032 09192 09332 09452 09554 0.9641 0.9713 0.9772 0.9821 0.986] 0.9893 0.9918 0.9938 0.9953 0.9965 0.9974 0.998] 0.9987 0.9990 0.9993 0.9995 0.9997 0.01 0.5040 0.5438 0.5832 0.6217 | 0.6591 10.6950 10.7291 0.7611 0.7910 0.8186 0.8438 0.8665 10.8869 | 0.9049 0.9207 0.9345 0.9463 09564 0.9649 0.9719 0.9778 10.9826 0.9864 0.9896 0.9920 0.9940 0.9955 0.9966 | 0.9975 10.9982 | 0.9987 0.9991 0.9993 0.9995 0.9997 0.02 0.03 0.5080 0.5120 0.5478 0.5517 0.5871 0.5910 0.6255 0.6293 0.6628 0.6664 0.6985 0.7019 0.7324 0.7357 07642 0.7673 0.7939 0.7967 0.8212 0.8238 0.8461 0.8485 0.8686 0.8708 0.8888 0.8907 0.9066 0.9082 0.9222 0.9236 0.9357 0.9370 0.9474 0.9484 0.9573 0.9582 0.9656 0.9664 0.9726 0.9732 0.9783 0.9788 0.9830 0.9834 0.9868 0.9871 0.9898 0.9901 0.9922 0.9925 0.9941 0.943 0.9956 0.9957 0.9967 0.9968 0.9976 0.9977 0.9982 0.9983 0.9987 0.9988 0.9991 0.9991 0.9994 0.9994 0.9995 0.9996 0.9997 0.9997 0.04 05160 0.5557 05948 0.6.33] 0.6700 0.7054 0.7389 0.7704 0.7995 0.8264 0.8508 0.8729 0.8925 0.9099 0.9251 0.9382 09495 0.9591 0.9671 0.9738 0.9793 0.9838 0.9875 0.9904 0.9927 0.9945 0.9959 0.9969 0.9977 0.9984 0.9988 0.9992 0.9994 0.9996 0.9997 0.05 05199 0.5596 0.5987 0.6368 0.6736 0.7088 0.7422 0.7734 0.8023 0.8289 0.8531 0.8749 0.8944 0.9115 0.9265 0.9394 0.9505 0.9599 0.9678 0.9744 10.9798 0.9842 0.9878 0.9906 0.9929 0.9946 0.9960 0.9970 0.9978 0.9984 0.9989 0.9992 0.9994 0.9906 0.9997 0.06 0.5239 0.5636 0.6026 0.6406 10.6772 07123 0.7454 0.7764 0.8051 0.8315 0.8554 0.8770 0.8962 10.9131 10.9279 0.9406 0.9515 0.9608 0.9686 0.9750 0.9803 0.9846 10.9881 10.9909 0.9931 0.9948 0.9961 0.9971 10.9979 0.9985 10.9989 0.9992 0.9994 0.9996 0.9997 0.07 0.5279 0.5675 0.6064 0.6443 0.6808 07157 0.7486 0.7794 0.8078 0.8340 0.8577 0.8790 0.8980 0.9147 0.9292 0.9418 0.9525 0.616 0.9693 0.9756 0.9808 0.9850 0.9884 0.9911 0.9932 0.9949 0.9962 0.9972 0.9979 0.9985 0.9989 0.9992 0.9995 0.9996 0.9997 008 05319 0.5714 0.6103 0.6480 0.6844 07190 0.7517 0.7823 0.8106 0.8365 0.8599 0.8810 0.8997 09162 0.9306 09429 09535 0.9625 0.9699 0.9761 0.9812 09854 0.9887 0.9913 0.9934 0.9951 0.9963 0.9973 0.9980 0.9986 0.9990 0.9993 0.9995 0.9996 0.9997 0.00 05359 0.5753 0.6141 0.6517 0.6879 0.7224 0.7549 0.7852 0.8133 0.8389 0.8621 0.88.30 0.9015 0.9177 0.9319 0.9441 0.9545 0.9633 0.9706 0.9767 0.9817 0.9857 0.9890 0.99 16 0.9936 0.9952 0.9964 0.9974 0.9981 0.9986 0.9990 0.9993 0.9995 0.9997 0.9998