Question

QUESTION 23 Suppose a certain college has its own entrance exam, and scores on this exam follow a normal distribution with mean 150 and standard deviation 20. Bob's original score was 130. What percentage of the students taking this exam had scores that fell above Bob's scores? O 1.16% 2.93% 3.84% 4. Not enough information to tell.

Answer 1

Let X denotes the scores of a certain college.

X ~ N($\small \mu$=150, =20)

0

Then,

- N(0,1) o

Let Z X- T

Therefore, P(Z <) = (2) and (-2) =1-02)

Bob's score was 130.

We have to find P(X>130),

PX > 130) = 1- P(X < 130

                      

X- = 1-PC VI 130 – 150 20 o

                      

=1-PZ-1

                      

=1 - Φ(-1) =1-1+ Φ(1)

                                                       (Value from z table)

= Φ(1) = 0.8413-

The percentage of the students who had scores that fell above Bob's scores is 84% (Option 3).

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