Question

using the table, give the percentage associated with each unit of standard deviation in the standard normal curve to the nearest hundredth.
standard deviation percentage area
-1 to 0 %
0 to +1 %
0 to +2 %
0 to +3 %
-1 to +2 %

Explanation:

Step1: Find area for -1 to 0

The standard - normal curve is symmetric about \(x = 0\). The area from \(0\) to \(+ 1\) is the same as the area from \(-1\) to \(0\). Looking at the table, when \(x = 1.0\), the area \(A(x)=0.3413\). So the area from \(-1\) to \(0\) is \(34.13\%\).

Step2: Find area for 0 to +1

From the table, when \(x = 1.0\), the area \(A(x)=0.3413\), so the area from \(0\) to \(+1\) is \(34.13\%\).

Step3: Find area for 0 to +2

When \(x = 2.0\), from the table \(A(x)=0.4772\), so the area from \(0\) to \(+2\) is \(47.72\%\).

Step4: Find area for 0 to +3

When \(x = 3.0\), from the table \(A(x)=0.4987\), so the area from \(0\) to \(+3\) is \(49.87\%\).

Step5: Find area for -1 to +2

The area from \(-1\) to \(0\) is \(0.3413\) and from \(0\) to \(+2\) is \(0.4772\). The total area is \(0.3413 + 0.4772=0.8185\), or \(81.85\%\).

Answer:

-1 to 0: \(34.13\%\)
0 to +1: \(34.13\%\)
0 to +2: \(47.72\%\)
0 to +3: \(49.87\%\)
-1 to +2: \(81.85\%\)