Find z such that 20.3% of the standard normal curve lies to the right of z.
0.831
0.533
-0.533
-0.257
0.257
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion to give you the Z score.
0.831
To find the value of z such that 20.3% of the standard normal curve lies to the right of z, we can use the Z-table or a calculator.
1. Using the Z-table:
- The Z-table gives you the area to the left of a given z-value.
- Since we need to find a value to the right of z, we need to find the complement of 20.3% (100% - 20.3% = 79.7%) and then look up that value in the Z-table.
- Finding the closest value to 79.7% in the Z-table gives us the z-value corresponding to that area.
2. Using a calculator:
- If you have access to a calculator, you can use the inverse cumulative distribution function (invNorm) or similar functions to find the z-value that corresponds to the given area.
- Simply enter the area (complement of 20.3%, i.e., 79.7%) and the calculator will give you the z-value.
Let's use the Z-table to find the value of z such that 20.3% of the standard normal curve lies to the right of z.
Looking up the complement of 20.3% (79.7%) in the Z-table, the closest match we find is 0.771, which corresponds to a z-value of -0.257.
Therefore, the value of z such that 20.3% of the standard normal curve lies to the right of z is -0.257.