All language subtitles for 03 - Use the exponential distribution

- [Instructor] One of the most important pieces

of information you can learn about

your business operations is how long it takes

to perform a specific task.

For example, if you repair phone screens,

you might find that the average time

to repair is five minutes.

You can use the exponential distribution using

that average of five denoted here by lambda,

as part of the exponential distribution

to determine the probability of a specific time.

This is what the graph looks like.

And it may seem odd that the average time

of five only occurs about 7% of the time.

And the reason that's the case is

because there is the possibility of long times,

for example 20 or 25 minutes.

However, those long duration repairs are offset

by the much higher probability

of having a repair taking one, two, three, four,

or five minutes.

To see how this works in Excel,

I will switch over to our sample workbook.

I have opened our Excel sample file

and that is 04_03_Exponential.

You can find that in the Chapter Four folder

of the Exercise Files collection.

I have the average time, or lambda, in cell E1,

and I also have a table on the left

that will let me calculate the probability

of a specific number of minutes for a repair.

So I'll click in cell B2, type an equal sign,

and I will use the exponential distribution function,

that is expon.dist.

First, I need to know my X,

that is the value that I'm comparing.

So that's in cell A2, for this particular calculation,

then a comma.

The lambda is in cell E1, but I need to use one divided

by lambda, and that is a characteristic

of the exponential distribution.

If you don't divide one by lambda,

you will get very strange results.

So in cell B2, I'll type one divided by E1.

And because I want this value to remain constant,

the cell reference remain constant,

I'll press F4 on Windows, it's Command-T on the Mac,

then a comma, and I am looking

for the probability density function or point probability,

so I will highlight false for this final argument,

Press Tab, right parentheses and Enter.

And I get a probability of about 0.1637.

I can now copy this formula down to the remaining cells.

So I will click cell B2

and then double-click the fill handle

at the bottom right corner.

I know that my mouse pointer's in the right place

when it changes to a black cross, double-click,

and you can see that the formula has been copied down.

And I see the individual probabilities.

Now let's say that I want to calculate the probability

of getting a value between three and seven.

So I have already calculated my probabilities

for three here, and then seven here,

but because their point probabilities, I can't use them.

I need to use the cumulative function.

So I will go to cell E3, and then type an equal sign,

and I'm going to subtract the probability

of getting three or less from the probability

of getting seven or less.

So I'll start by calculating the value for seven,

that is the cumulative probability of getting seven or less.

So that's expon.dist, the value is seven, lambda,

and again, it needs to be one divided by lambda,

that's in E1.

I'm not going to copy the formula, so I won't worry

about a cell reference, and it is cumulative.

So I will highlight true, which it already is,

and then press Tab to get that, then right parentheses

and I will subtract the same calculation

for the number three.

I'll go through it a little bit more quickly.

Exponential distribution, three, one divided by E1,

comma, cumulative true, right parentheses and Enter.

And I get 30.22%.

So the probability of getting a value

between three and seven, inclusive, is 30.22%,

or about a the third of the time.

And that makes sense with an average of five.