00:01
In this question we are told that the demand for regular gasoline during the lead time, it's called this random variable x, is normally distributed with a mean of 930 gallons and a standard deviation of 140 gallons.
00:15
And for the first question we were asked for the probability that the demand during the next lead time will be less than 800 gallons.
00:24
So this is the probability that x is smaller than 800.
00:29
This graph represents our normal distribution for gasoline demand.
00:33
We have a mean of 930, which would be right in the center.
00:37
Standard deviation of 140.
00:40
800 is approximately here.
00:44
Probability that the lead time, or that the demand for gasoline during the lead time, is less than 800, is equal to the area under the curve, and to the left of 800.
00:55
That corresponds to the area of this blue shaded region.
00:59
Now we can use excel to solve this problem.
01:01
In excel, we can use the normal distribution function.
01:04
So we start with an equal sign, type the norm .dist function.
01:09
For the first argument we enter 800, and then we enter the mean and the standard deviation.
01:16
For the cumulative argument, we enter true because we want the probability that x is anything less than 800.
01:22
We hit enter, and we get a probability of .1766 approximately.
01:32
And the second question is similar, except we want the probability that the demand is less than a thousand.
01:40
So we can do this one in excel 2.
01:42
We can actually recycle the last formula we used by entering 1 ,000 instead of 800 for the first argument.
01:51
All the other arguments remain the same.
01:54
We get a probability of 0 .6915.
02:04
For the third question, we are asked for the probability that during the next lead time, the demand will be equal to 900 gallons exactly.
02:13
This is the probability that x is equal to 0, is equal to 900.
02:20
And for any continuous random variable, a normal random variable is continuous.
02:26
The probability of any exact number is always zero...