Given that z is a standard normal random variable, find z for each situation (to 2 decimals).
1.The area between -z and z is 0.2128
Use "areas under normal distribution" table in the back of your statistics text.
To find the value of z for which the area between -z and z is 0.2128, we can use the standard normal distribution table.
Step 1: Draw a standard normal curve and shade the area between -z and z.
Step 2: Since the area between -z and z is given as 0.2128, we want to find the z-values that correspond to this area on the standard normal curve.
Step 3: Look up the area 0.2128 in the standard normal distribution table. The table provides the area to the left of a particular z-value. Since we want the total area between -z and z, we need to find the z-values that correspond to an area of 0.2128 on both sides of the mean (symmetrically).
Step 4: Find the closest value in the table to 0.2128. In the table, the closest value to 0.2128 is 0.80. This corresponds to a z-value of approximately -0.84 (the negative sign indicates the area to the left of the mean).
Step 5: Note that the table gives the area to the left of the z-value. To get the area between -z and z, we need to find the area to the left of z (0.84) as well. The area to the left of 0.84 in the table is 0.7995.
Step 6: Subtract the area to the left of z from 0.5 (the area to the left of the mean). 0.5 - 0.7995 = -0.2995.
Therefore, the z-value for which the area between -z and z is 0.2128 is approximately -0.84.