Below are the durations (in minutes) of 40 eruptions of the geyser Old Faithful in Yellowstone National Park.
4.1 |
1.8 |
3.2 |
1.9 |
4.6 |
2.0 |
4.5 |
3.9 |
4.3 |
2.3 |
3.8 |
1.9 |
4.6 |
1.8 |
4.7 |
1.8 |
4.6 |
1.9 |
3.5 |
4.0 |
3.7 |
3.7 |
4.3 |
3.6 |
3.8 |
3.8 |
3.8 |
2.5 |
4.5 |
4.1 |
3.7 |
3.8 |
3.4 |
4.0 |
2.3 |
4.4 |
4.1 |
4.3 |
3.3 |
2.0 |
Construct a normal probability plot for these data. Do the data appear to come from an approximately normal distribution?
Solution :
Step 1 of 1:
Given the below are the duration in minute of 40 eruptions of geyser old faithful in yellowstone national park.
Here n=40.
Our goal is:
We need to construct a normal probability plot for these data and
We need to find do these data appear to come from an approximately normal population.
Now we have to find the normal probability plot for these data .
The formula of the cumulative probability is
=
Where i = 1,2,3,...,40.
And n=40.
We are using excel to plot the normal probability.
Then we sorted values.
We are using =NORMSINV function to find the .
=NORMSINV(0.0125)
Then we get value is -2.241402728.
The data is given below.
i |
|
|
|
i |
|
|
|
1 |
1.8 |
0.0125 |
-2.241402728 |
21 |
3.8 |
0.5125 |
0.031337982 |
2 |
1.8 |
0.0375 |
-1.780464342 |
22 |
3.8 |
0.5375 |
0.094137414 |
3 |
1.8 |
0.0625 |
-1.534120544 |
23 |
3.8 |
0.5625 |
0.157310685 |
4 |
1.9 |
0.0875 |
-1.356311745 |
24 |
3.8 |
0.5875 |
0.221118713 |
5 |
1.9 |
0.1125 |
-1.213339622 |
25 |
3.9 |
0.6125 |
0.285840875 |
6 |
1.9 |
0.1375 |
-1.091620367 |
26 |
4 |
0.6375 |
0.351784345 |
7 |
2 |
0.1625 |
-0.98423496 |
27 |
4 |
0.6625 |
0.419295753 |
8 |
2 |
0.1875 |
-0.887146559 |
28 |
4.1 |
0.6875 |
0.488776411 |
9 |
2.3 |
0.2125 |
-0.797776846 |
29 |
4.1 |
0.7125 |
0.560703032 |
10 |
2.3 |
0.2375 |
-0.71436744 |
30 |
4.1 |
0.7375 |
0.635657014 |
11 |
2.5 |
0.2625 |
