The area that lies between $$ z=-1.57 $$ and $$ z=-2.07 $$ is (Round to four decimal places as needed.)

Question

UpStudy AI · Accepted Answer

Let the area $$ A $$ between $$ z = -2.07 $$ and $$ z = -1.57 $$ be given by

$$
A = P(-2.07 \leq z \leq -1.57) = \Phi(-1.57) - \Phi(-2.07)
$$

where $$ \Phi(z) $$ is the cumulative distribution function (CDF) of the standard normal distribution.

Using the symmetry of the normal distribution, we know

$$
\Phi(-x) = 1 - \Phi(x)
$$

Thus,

$$
\Phi(-1.57) = 1 - \Phi(1.57) \quad \text{and} \quad \Phi(-2.07) = 1 - \Phi(2.07)
$$

Suppose from the standard normal table we have:

$$
\Phi(1.57) \approx 0.9418 \quad \text{and} \quad \Phi(2.07) \approx 0.9808
$$

Then,

$$
\Phi(-1.57) \approx 1 - 0.9418 = 0.0582
$$
$$
\Phi(-2.07) \approx 1 - 0.9808 = 0.0192
$$

Now, the area is

$$
A \approx 0.0582 - 0.0192 = 0.0390
$$

Thus, the area that lies between $$ z = -1.57 $$ and $$ z = -2.07 $$ is approximately $$ 0.0390 $$.
The area between $$ z = -1.57 $$ and $$ z = -2.07 $$ is approximately 0.0390.

The area that lies between and is
(Round to four decimal places as needed.)

Upstudy AI Solution

Answer

Solution

Bonus Knowledge

Related Questions

Latest Statistics Questions

The area that lies between and is (Round to four decimal places as needed.)