next up previous contents index
Next: Calculating Areas under the Up: Binomial and Normal Distributions Previous: Binomial and Normal Distributions

   
Computing Probabilities Using the Normal Curve

The electronics store TVs and More wants to know how many large screen television sets to order for the next monthly delivery. Past data show that this time of year, they sell an average of 36 large screen television sets per month, with a standard deviation of 8.

Problem 1. If they order 40 sets, what is the probability that they will run out of stock?
Problem 2. Given the cost of running out of stock and the storage cost of keeping too many, the manager decides to order enough TV sets to cover customer demands 90% of the time, i.e there should be 10% or less likelihood that they run out of stock. How many should they order?

Knowing the average and SD of a process ($36 \pm 8$) gives us some understanding of what to expect. However, the sales situation above requires the computation of probabilities , or chances, as in the ``chance of demand exceeding 40''. This is where the normal curve  is helpful. If the demand variable histogram is approximately bell-shaped, then the desired probability (area to the right of 40 under histogram) may be approximated using the normal curve (area to the right of 40 under normal curve). See the two graphs in Figure  4.1.


  
Figure 4.1: Probability of Demand Exceeding 40
\begin{figure}
\begin{center}
\epsfig{file=Nhist368.ps, width=2.8in, angle=-90}\epsfig{file=over402.ps, width=3in, angle=-90}\end{center}\end{figure}

By ``demand following the normal curve'', we mean that in repeated observations past, present and future, the histogram of demand for TV sets will look like the histogram on the left of Figure  4.1. Or that the stem and leaf plot  of n=100 future observations should look like Figure  4.2


  
Figure 4.2: Stem-and-leaf of idealized normal curve demand data (mean=36, SD=8)
\begin{figure}
\begin{tex2html_preform}\begin{verbatim}1 6
1 89
2 012
2 34455...
...55566
4 77889
5 012
5 34
5 6\end{verbatim}\end{tex2html_preform}\end{figure}

Sometimes, we do have data-based evidence that the data histogram or stem-and-leaf will look like the normal curve. Height and GPA, for instance, is known to follow the normal curve quite closely (with documentation in published sources). At other times, we may need to rely on the normality assumption without the hard evidence, because it is often the easiest way to compute, at least approximately, desired probabilities. In any case, probabilities based on the normal curve should be treated as approximations of the true probabilities anyway.



 
next up previous contents index
Next: Calculating Areas under the Up: Binomial and Normal Distributions Previous: Binomial and Normal Distributions

2003-09-08