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 z2 and z2 ​(or within 2 standard deviations of the​ mean). About nothing​% of the area is between z2 and z2 ​(or within 2 standard deviations of the​ mean).

Answer 1

95%

Explanation:

About 95% of the area is within two standard deviation in standard normal distribution. This can be explained by finding the probability within 2 standard deviation using standard normal distribution.

P(z1<Z<z2)=P(-2<Z<2)

P(-2<Z<2)=P(-2<Z<0)+P(0<Z<2)

P(-2<Z<2)=0.4772+0.4772

P(-2<Z<2)=0.9544

Thus, About 95% of the area is between z2 and z2