The amount of fill (weight of contents) put into a glass jar of spaghetti sauce is normally distributed with mean u = 843 grams and standard deviation of o = 11 grams. (a) Describe the distribution of x, the amount of fill per jar. O skewed right O normal O skewed left O chi-square (b) Find the probability that one jar selected at random contains between 842 and 865 grams. (Give your answer correct to four decimal places.) (c) Describe the distribution of x, the mean weight for a sample of 20 such jars of sauce. O skewed right O normal O skewed left O chi-square (d) Find the mean of the x distribution. (Give your answer correct to the nearest whole number.) (ii) Find the standard error of the x distribution. (Give your answer correct to two decimal places.) (e) Find the probability that a random sample of 20 jars has a mean weight between 842 and 865 grams. (Give your answer correct to four decimal places.)
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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