4. Suppose you would like to keep a test tube at 48°F (exactly), but that your refrigeration unit exhibits some random fluctuations, so that the difference between the temperature at which you set the thermostat and the true temperature is distributed normally with mean 0 and variance 1.96. What is the highest you can set the thermostat and be 95% sure that the true temperature is no more than 48°? (Use Table 5.1 or the distributed table in class to get values for , so that the answers are more consistent.
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!
4
Table 5.1 is just the standard normal table for Z but rounded to 4 decimal places. Thank you!
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