91影视

The z-scores are -1 and 1.

Let Z be the random variable following the standard normal distribution.

Thus,

$$\begin{gathered} Z~N\left(渭,{蟽}^2\right) \\ ~N\left(0,1^2\right) \end{gathered}$$

Steps to draw a normal curve:

1. Make a horizontal axis and a vertical axis.
2. Mark the points -3.5, -3.0, -2.0 up to 3 on the horizontal axis and points 0, 0.05, 0.10 up to 0.50 on the vertical axis.
3. Provide titles to the horizontal and vertical axes as 鈥榸鈥� and 鈥楶(z)鈥�, respectively.
4. Shade the region between -1 and 1.

The shaded area of the graph indicates the probability that the z-score is between -1 and 1.

The area under the curve has a one-to-one correspondence with the probability.

The area between -1 and 1 is computed as

$P\left(-1<Z<1\right)=P\left(Z<1\right)-P\left(Z<-1\right)鈥�鈥�鈥�鈥�鈥�鈥�鈥�鈥�鈥�鈥�鈥�鈥�鈥�鈥�鈥�鈥�鈥�鈥�...\left(1\right)$

Referring to the standard normal table,

• the cumulative probability of -1 is obtained from the cell intersection for rows -1.0 and the column value 0.00, which is 0.1587, and
• the cumulative probability of 1 is obtained from the cell intersection for rows 1.0 and the column value 0.00, which is 0.8413.

Thus,

$$\begin{gathered} P\left(Z<1\right)=0.8413 \\ P\left(Z<-1\right)=0.1587 \end{gathered}$$

Substituting in equation (1),

$$\begin{gathered} P\left(-1<Z<1\right)=P\left(Z<1\right)-P\left(Z<-1\right) \\ =0.8413-0.1587 \\ =0.6826 \end{gathered}$$

Thus, the area between -1 and 1 is 0.6826.

The area can be expressed as

Thus,about 68.26 % of the area is between z = -1 and z = 1.