Question

Find the area, to the nearest thousandth, of the standard normal distribution between the given z-scores.z = 1 and z = 1.81

Answer 1

Since this is a normal distribution, the area between the z-scores z₁ = 1 and z₂ = 1.81 is just the probability that the random variable Z is between z₁ and z₂:

`P(z_1\leq Z\leq z_2)=P(z_1\leq Z)-P(z_2\leq Z_{})=P(1\leq Z)-P(1.81\leq Z)`

Using the values reported on tables for the standardized normal distribution, we know that:

`\begin{gathered} P(1\leq Z)=0.158655 \\ P(1.81\leq Z)=0.035148 \end{gathered}`

Now, using these results:

`P(z_1\leq Z\leq z_2)=0.158655-0.035148=0.123507`