A cheese processing company wants to estimate the mean cholesterol content of all one-ounce servings of a type of cheese. The estimate must be within 0.76 milligram of the population mean. (a) Determine the minimum sample size required to construct a 95% confidence interval for the population mean. Assume the population standard deviation is 3.05 milligrams. (b) The sample mean is 28 milligrams. Using the minimum sample size with a 95% level of confidence, does it seem likely that the population mean could be within 3% of the sample mean? within 0.3% of the sample mean? Explain. Click here to view page 1 of the Standard Normal Table Click here view page 2 of the Standard Normal Table (a) The minimum sample size required to construct a 95% confidence interval is servings. (Round up to the nearest whole number.) (b) The 95% confidence interval is ( )I V seem likely that the population mean could be within 3% of the sample mean because 3% off from the sample mean would fall v the confidence interval. It V seem likely that the population mean could be within 0.3% of the sample mean because 0.3% off from the sample mean would fall V the confidence interval. (Round to two decimal places as needed.)
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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