Question

Find the indicated area under the curve of the standard normal​ distribution, then convert it to a percentage and fill in the blank.

About_____% of the area is between z = 2.2 and z = 2.2 (or within 2.2 standard deviations of the mean).
About_____% of the area is between z = 2.2 and z = 2.2 (or within 2.2 standard deviations of the mean).

Answer 1

Complete Question

Find the indicated area under the curve of the standard normal​ distribution, then convert it to a percentage and fill in the blank.

About_____% of the area is between z = - 2.2 and z = 2.2 (or within 2.2 standard deviations of the mean).

About_____% of the area is between z = - 2.2 and z = 2.2 (or within 2.2 standard deviations of the mean).

Answer:

About 97.219% of the area is between z = - 2.2 and z = 2.2 (or within 2.2 standard deviations of the mean).

Explanation:

From the question given we can see that they both are the same so 1 will just solve one

Now the area under this given range can be represented mathematically as

`P ( -2.2 < z < 2.2) = P(z < 2.2 ) - P(z < -2.2 )`

Now from the z-table

`p(z < 2.2 ) = 0.9861`

and

`p(z < - 2.2 ) = 0.013903`

So

`P ( -2.2 < z < 2.2) = 0.9861 - 0.013903`

`P ( -2.2 < z < 2.2) = 0.97219`

So converting to percentage

`P ( -2.2 < z < 2.2) = 0.97219 * 100`

`P ( -2.2 < z < 2.2) = 97.219 \%`