16. Find the z-score for which 99% of the distribution's area lies between - z and z.
You can play around with Z table stuff at
http://davidmlane.com/hyperstat/z_table.html
To find the z-score for which 99% of the distribution's area lies between -z and z, we need to divide the remaining area (1% or 0.01) into two equal parts.
Since the normal distribution curve is symmetrical, we can find the z-score for the middle 0.005 (0.01/2) in the tail of the distribution on either side.
To find this z-score, we can use a standard normal distribution table (also known as a z-table) or a statistical calculator.
Using a standard normal distribution table:
1. Look for the value closest to 0.005 in the body of the table. The closest value is 0.0055.
2. Identify the corresponding z-score in the first column of the table. The z-score is approximately -2.58.
This means that 99% of the area under the standard normal curve lies between -2.58 and 2.58.
Therefore, the z-score for which 99% of the distribution's area lies between -z and z is approximately 2.58.