91影视

z is the standard normal variable.

$$\begin{gathered} \mathrm{a}. \\ P\left(-1鈮�z鈮�1\right)=P\left(z鈮�1\right)-P\left(z<-1\right) \\ =桅\left(1\right)-桅\left(-1\right) \\ =0.841345-0.158655 \\ =0.682689 \\ 饾啅0.6827 \end{gathered}$$

From the standard normal table, we get this probability$P\left(-1鈮�z鈮�1\right)=0.6827$

Therefore, the required probability is 0.6827.

$$\begin{gathered} P\left(-1.96鈮�z鈮�1.96\right)=P\left(z鈮�1.96\right)-P\left(z<-1.96\right) \\ =桅\left(1.96\right)-桅\left(1.96\right) \\ =0.975002-0.024998 \\ =0.950004 \\ 饾啅0.95 \end{gathered}$$

From the standard normal table, we get this probability$P\left(-1.96鈮�z鈮�1.96\right)=0.95$

Therefore, the required probability is 0.95.

c.

$$\begin{gathered} P\left(-1.645鈮�z鈮�1.645\right)=P\left(z鈮�1.645\right)-P\left(z<-1.645\right) \\ =桅\left(1.645\right)-桅\left(-1.645\right) \\ =0.950015-0.049985 \\ =0.90003 \\ 饾啅0.90 \end{gathered}$$

From the standard normal table, we get this probability$P\left(-1.645鈮�1.645\right)=0.90$

Therefore, the required probability is 0.90.

d.

$$\begin{gathered} \mathrm{P}\left(-2鈮�\mathrm{z}鈮�2\right)=\mathrm{P}\left(\mathrm{z}鈮�2\right)-\mathrm{P}\left(\mathrm{z}<-2\right) \\ =\mathrm{桅}\left(2\right)-\mathrm{桅}\left(-2\right) \\ =0.97725-0.02275 \\ =0.9545 \end{gathered}$$

From the standard normal table, we get this probability$P\left(-2鈮�z鈮�2\right)=0.9545$

Therefore, the required probability is 0.9545.