(a) Use a computer program to find the probabilitythat a random variable having the normal distributionwith the mean −1.786 and the standard deviation 1.0416will assume a value between −2.159 and 0.5670.(b) Interpolate in the standard normal distribution tableto find this probability and compare your result with themore exact value found in part (a).
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!
(a) Use a computer program to find the
that a random variable having the
with the mean −1.786 and the standard deviation 1.0416
will assume a value between −2.159 and 0.5670.
(b) Interpolate in the standard normal distribution table
to find this probability and compare your result with the
more exact value found in part (a).
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