Answer:
a) 0.1587 (or 15.87%)
b) 0.0478 (or 4.78%)
c) 0.7935 (or 79.35%)
Step-by-step explanation:
Find the following probabilities:
(a) the thickness is less than 3.0 mm
We need to find the area under the Normal curve with a mean of 4.5 mm and a standard deviation of 1.5 mm to the left of 3 mm
(See picture 1 attached)
We can do that with the help of a calculator or a spreadsheet.
In Excel use
NORMDIST(3,4.5,1.5,1)
In OpenOffice Calc use
NORMDIST(3;4.5;1.5;1)
and we get the value 0.1587 (or 15.87%)
(b) the thickness is more than 7.0 mm
Now we need the area to the right of 7 (1 - the area to the left of 7)
(See picture 2 attached)
In Excel use
1-NORMDIST(7,4.5,1.5,1)
In OpenOffice Calc use
1-NORMDIST(7;4.5;1.5;1)
and we get the value 0.0478 (or 4.78%)
(c) the thickness is between 3.0 mm and 7.0 mm
We are looking for the area between 3 and 7
(See Picture 3)
Since the area under the Normal equals 1, we have
Area to the left of 3 + Area between 3 and 7 + Area to the right of 7 = 1
Hence,
0.1587 + Area between 3 and 7 + 0.0478 = 1
and
Area between 3 and 7 = 1 - 0.1587 - 0.0478 = 0.7935 (or 79.35%)
