Question

for exercises 7 through 26, find the area under the standard normal distribution curve.

1. between ( z = 0 ) and ( z = 0.98 )
2. between ( z = 0 ) and ( z = 1.77 )
3. between ( z = 0 ) and ( z = - 2.14 )
4. between ( z = 0 ) and ( z = - 0.32 )
5. to the right of ( z = 0.29 )
6. to the right of ( z = 2.01 )
7. to the left of ( z = - 1.39 )

Explanation:

Step1: Use the standard normal distribution table

The area between \(z = 0\) and \(z=a\) (\(a>0\)) is given by \(\varPhi(a)-\varPhi(0)\), where \(\varPhi(z)\) is the cumulative distribution function of the standard normal distribution. And \(\varPhi(0) = 0.5\).
For \(z = 0.98\), from the standard - normal table \(\varPhi(0.98)=0.8365\). Then the area between \(z = 0\) and \(z = 0.98\) is \(0.8365 - 0.5\).

Step2: Calculate the area

\(0.8365-0.5=0.3365\)

Answer:

\(0.3365\)