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!
Ballistics Ballistics experts are able to identify the
weapon that fired a certain bullet by studying the markings on the bullet after it is fired. They test the rifling
(the grooves in the bullet as it travels down the barrel
of the gun) by comparing it to that of a second bullet
fired into a bale of paper. The speed, s, in centimeters per second, that the bullet travels through the paper is
given by s = 3013 - 10t2 3
, where t is the time after
the bullet strikes the bale and t … 0.3 second.
a. Complete the following table to find the speed for
given values of t.
b. Use the root method to find the number of seconds
to give s = 0. Does this agree with the data in the
table?
Step by step
Solved in 3 steps
