More cereal In Exercise 47 we poured a large and asmall bowl of cereal from a box. Suppose the amount ofcereal that the manufacturer puts in the boxes is a randomvariable with mean 16.2 ounces and standard deviation0.1 ounces.a) Find the expected amount of cereal left in the box.b) What’s the standard deviation?c) If the weight of the remaining cereal can be describedby a Normal model, what’s the probability that the boxstill contains more than 13 ounces?
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!
More cereal In Exercise 47 we poured a large and a
small bowl of cereal from a box. Suppose the amount of
cereal that the manufacturer puts in the boxes is a random
variable with mean 16.2 ounces and standard deviation
0.1 ounces.
a) Find the expected amount of cereal left in the box.
b) What’s the standard deviation?
c) If the weight of the remaining cereal can be described
by a Normal model, what’s the
still contains more than 13 ounces?
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