You may need to use the appropriate appendix table or technology to answer this question. According to Reader's Digest, 42 percent of primary care doctors think their patients receive unnecessary medical care. (=) Suppose a sample of 315 primary care doctors was taken. Show the sampling distribution of the proportion of the doctors who think their patients receive unnecessary medical care. P -0.06 -0.03 0 0.03 0.06 0.36 0.39 0.42 0.45 0.48 -0.03 0 0.03 0.06 0.09 -1.58 -0.58 0.42 1.42 2.42 OX (b) What is the probability that the sample proportion will be within 10.03 of the population proportion? (Round your answer to four decimal places.) D.6 158 1x (c) What is the probability that the sample proportion will be within 10.05 of the population proportion? (Round your answer to four decimal places.) 0.8502 1 X (d) what would be the effect of taking a larger sample on the probabilities in parts (b) and (c)? Why? The probabilities would decrease because the standard errors would be larger. O The probabilities would increase because the standard errors would be smaller. The probabilities would increase because the standard errors would be larger. O The probabilities would decrease because the standard errors would be smaller. X