TABLE 1 CUMULATIVE PROBABILITIES FOR THE STANDARD NORMAL DISTRIBUTION (Continued) Cumulative probability Entries in the table give the area under the curve to the left of the z value. For example, for z = 1.25, the cumulative probability is .8944. 0 2 2 .00 .01 .02 .03 .04 .05 .06 .07 .08 5000 .5040 5080 .5120 5160 5239 .5279 .5319 .5359 According to Reader's Digest, 40%% of primary care doctors think their patients receive unnecessary medical care. Use z-table. .5398 .5438 .5478 .5517 .5557 .5596 5636 5675 .5753 a. Suppose a sample of 350 primary care doctors was taken. Show the sampling distribution of the proportion of the doctors who think their 5832 5910 5987 6026 .6064 patients receive unnecessary medical care. 6217 .6255 6293 6331 6368 .6480 6517 A 6554 6591 .6628 .6664 6700 6736 6772 6808 6844 6879 E(p) = 0.32 of - (to 4 decimals) .6915 .6950 .6985 .7019 .7054 .7123 7190 .7224 .7257 .7291 .7324 .7357 .7389 .7422 .7454 .7486 .7517 .7549 b. What is the probability that the sample proportion will be within 10.03 of the population proportion. Round your answer to four decimals. 7580 .7642 .767 .7704 .7764 .7794 .7823 .7852 7910 .7939 .8023 .8051 .8078 .8106 .8133 8159 .8212 .8238 8264 8289 .8315 8340 8365 .8389 c. What is the probability that the sample proportion will be within 10.05 of the population proportion. Round your answer to four decimals. 1.0 .8413 .8485 8531 .8577 .8599 1.1 .8643 8665 .8686 8729 .8749 8790 .8810 .8830 d. What would be the effect of taking a larger sample on the probabilities in parts (b) and (c)? Why? 1.2 .8849 886 8925 .8962 .8980 .8997 The probabilities would |increase v . This is because the increase in the sample size makes the standard error, Up , .9032 9049 9066 .9099 .9131 .9162 1.4 9192 9207 9222 .9236 .9251 9265 .9292 9306 9319 smaller 1.5 .9332 9357 .9370 .9382 9394 9406 .9429 .9441 1.6 .9452 9474 .9484 .9505 .9515 9535 1.7 .9554 .9564 9573 .9591 9599 .9608 .9616 9625 9633 1.8 .9641 9649 .9656 .9664 9671 9678 9686 .9693 9699 .9706 1.9 .9713 9719 .9726 9738 9744 9756 2.0 .9772 9783 9788 9793 9798 .9812 .9817 2.1 .9821 .9826 .9830 .9834 9842 .9846 .9850 .9854 2.2 .9861 9868 .9871 .9875 9881 9884 9887 9890 2.3 9893 9896 9898 9906 9911 9916 2.4 9920 9922 .9925 9927 9929 .9931 .9932 9934 9936 2.5 .9940 .9941 .9943 9945 9949 .9951 9952 2.6 9953 9955 9956 .9957 9959 9960 9962 9963 9964 2.7 9965 9966 9967 .9968 9969 9970 9971 9973 9974 2.8 .9974 997 9977 9978 .9979 .9979 .9980 9981 29 .9981 .9982 .9982 .9983 .9984 .9984 9985 .9986 9986 3.0 .9987 .9987 .9988 9989 .9989 9990