Purchases made at small "corner stores" were studied by the authors of a certain paper. Corner stores were defined as stores that are less than 200 square feet in size, have only one cash register, and primarily sell food. After observing a large number of corner store purchases in Philadelphia, the authors reported that the average number of grams of fat in a corner store purchase was 21.3. Suppose that the variable x = number of grams of fat in a corner store purchase has a distribution that is approximately normal with a mean of 21.3 grams and a standard deviation of 7 grams. (Round your answers to four decimal places.)   What is the probability that a randomly selected corner store purchase has between 15 and 25 grams of fat? If two corner store purchases are randomly selected, what it the probability that both of these purchases will have more than 25 grams of fat?

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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!