3An HP laser printer is advertised to print text documents at a speed of 18 ppm (pages per minute). The manufacturer tells you that the printing speed is actually a Normal random variable with a mean of 17.57 ppm and a standard deviation of 3 ppm. Suppose that you draw a random sample of 11 printers. Part i) Suppose the number of printers drawn is quadrupled. How will the standard deviation of sample- mean printing speed change? A. It will increase by a factor of 4. B. It will decrease by a factor of 4. C. It will decrease by a factor of 2. D. It will increase by a factor of 2. E. It will remain unchanged. Part ii) Suppose the number of printers drawn is quadrupled. How will the mean of the sample mean printing speed change? A. It will increase by a factor of 4. B. It will decrease by a factor of 4. C. It will decrease by a factor of 2. D. It will increase by a factor of 2.
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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