The length of certain bricks is a random variablewith a mean of 8 inches and a standard deviation of0.1 inch, and the thickness of the mortar between twobricks is a random variable with a mean of 0.5 inchand a standard deviation of 0.03 inch. What is themean and the standard deviation of the length of awall made of 50 of these bricks laid side by side, if wecan assume that all the random variables involved areindependent?
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!
The length of certain bricks is a random variable
with a
0.1 inch, and the thickness of the mortar between two
bricks is a random variable with a mean of 0.5 inch
and a standard deviation of 0.03 inch. What is the
mean and the standard deviation of the length of a
wall made of 50 of these bricks laid side by side, if we
can assume that all the random variables involved are
independent?
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