You may need to use the appropriate appendix table or technology to answer this question. A researcher reports survey results by stating that the standard error of the mean is 25. The population standard deviation is 575. (a) How large was the sample used in this survey? :l (b) What is the probability that the sample mean was within i25 of the population mean? (Round your answer to four decimal places.) E You may need to use the appropriate appendix table or technology to answer this question. The president of Doerman Distributors, Inc., believes that 35% of the rm's orders come from rst-time customers. A random sample of 100 orders will be used to estimate the proportion of rsttime customers. (3) Assume that the president is correct and p = 0.35. What is the sampling distribution of}; for n = 100? (Round your answer for a, to four decimal places.) p (5;: mm =: Since np = :l and n(1 p) = :l , approximating the sampling distribution with a normal distribution appropriate in this case. (b) What is the probability that the sample proportion B will be between 0.25 and 0.45? (Round your answer to four decimal places.) 3 (c) What is the probability that the sample proportion will be between 0.30 and 0.40? (Round your answer to four decimal places.) E