4. Final: A filling process is supposed to fill jars with 16 ounces of grape jelly. Specifications state that each jar must contain betweern 15.95 ounces and 16.05 ounces. A jar is selected from the process every half hour until a sample of 100 jars is obtained. When the fills of the jars are measured, it is found that x (xbar) = 16.0024 and s = .02454. Using x"(xbar) and s as point estimates of u (meu) and o (sigma), estimate the probability that a randomly selected jar will have a fill, x, and that is less than minimum reading. Assume that the process is in control and that the population of all jar fills is normally distributed. O a. .0391 O b. .0411 O c.0229 O d. .0166 O e. None of the above
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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