If Z is a standard normal random variable, find the value

Step 1 of 4

(a)

If Z is a standard normal random variable, find the value \(z_{0}\) such that

\(P\left(Z>z_{0}\right)=0.5\)

In Table 4, Appendix 3, we have given the tabulated areas (probability) are to the right of points z, where z is the distance from the mean, measured in standard deviations.

\(P\left(Z>z_{0}\right)=\text { area to the right points of } z_{0}=0.5\)

Hence we will check the value of \(z_{0}\) from Table 4, Appendix 3, for which the area or \(P\left(Z>z_{0}\right)\)

Will be 0.5.

From the normal distribution table, we can see that the value of \(z_{0}\) is 0.

Hence the value of \(z_{0}\) is 0.