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 zequalsnegative 1 and zequals1 ​(or within 1 standard deviation of the​ mean).

Answer 1

68.28% of data lies under the curve between z equals -1 and z equals 1 ​.

Explanation:

We are given the following in the question:

We are given a standard normal distribution.

We have to find the area under the curve between z equals -1 and z equals 1 ​that is within one standard deviation.

Empirical Formula:

• Almost all the data lies within three standard deviation from the mean for a standard normally distributed data.
• About 68.27% of data lies within one standard deviation from the mean.
• About 95.44% of data lies within two standard deviations of the mean.
• About 99.73% of data lies within three standard deviation of the mean.

Thus, from Empirical formula 68.28% of data lies under the curve between z equals -1 and z equals 1 ​.