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The pn'ceeamings ratios for all companies whose shares are traded on a specic stock exchange follow a normal distribution with a standard deviation of 4.1. A random sample of these companies is selected in order to estimate the population mean pn'ceeamings ratio. Complete parts {a} Through (c). a. How large a sample is necessary in order to ensure that the probability that the sample mean differs from the population mean by more than 1.0 is less than 0.05? The sample size must be at least . [Type a whole number.)