Total fat content (including saturated fat and trans fats) is a key characteristic of cheese. Assume that for a given type of cheese, total fat content (10-1 g/g of cheese) follows a normal distribution with a population mean of 2.85 (unit) and population variance of 0.01 (unit2). Such an assumption is reasonable because fat content varies inside cheese and the 'errors ' around the mean total fat content (i.e. the value appearing on the etiquette) are distributed like a bell shape. Condition: Twenty-five (non-statistical) samples of 1 g of cheese drawn from the same container were analyzed for total fat content. In other words, i.i.d. random sample of size 25 was collected from a normal population of cheese total fat contents with the parameter values given.
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!
Total fat content (including saturated fat and trans fats) is a key characteristic of cheese. Assume that for a given type of cheese, total fat content (10-1 g/g of cheese) follows a
Condition: Twenty-five (non-statistical) samples of 1 g of cheese drawn from the same container were analyzed for total fat content. In other words, i.i.d. random sample of size 25 was collected from a normal population of cheese total fat contents with the parameter values given.
1)Calculate the probability that the sample mean takes a value smaller than 2.825 (unit).
2)Calculate the median of the sample variance.
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