Many college graduates who are employed full-time have longer than 40-hour work weeks. Suppose that we wish to estimate the mean number of hours, u, worked per week by college graduates employed full-time. We'll choose a random sample of college graduates employed full-time and use the mean of this sample to estimate u. Assuming that the standard deviation of the number of hours worked by college graduates is 6.20 hours per week, what is the minimum sample size needed in order for us to be 95% confident that our estimate is within 1.2 hours per week of u? Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements). (If necessary, consult a list of formulas.)
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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