You may need to use the appropriate appendix table or technology to answer this question. The president of Doerman Distributors, Inc., believes that 30% of the rm's orders come from rst-time customers. A random sample of 150 orders will be used to estimate the proportion of rst-time customers. (a) Assume that the president is correct and p = 0.30. What is the sampling distribution of; for n = 150? (Round your answer for a"; to four decimal places.) a; = 0.0374 v 5(5) = 0.9925 x Since np = 0.3 x and n(1 p) = 0.3 x , approximating the sampling distribution with a normal distribution is v 'I appropriate in this case. (b) What is the probability that the sample proportion B will be between 0.20 and 0.40? (Round your answer to four decimal places.) 0.9925 (c) What is the probability that the sample proportion will be between 0.25 and 0.35? (Round your answer to four decimal places.) 0.8186 4